Technically, for a logician, or a semanticist of the
Snow-is-White school, tautologies convey no information; but to linguists and pragmaticians, in
context they often do. In fact, we
may state that they usually do, since
otherwise why utter them?
“Business is business” is flint-hearted; “Boys will be boys”, tenderly exculpatory.
The opposite of an utterance that pretends to contain no
information (and thus, in particular, to be inexpugnable) but actually does
(and often of a trenchant sort), is a definition that, ex cathedra, is all
about informing, but which melts to the touch. Cf. our essay here:
~
Covertly vacuous uses of technical-sounding terms have been scouted in histories of science. As, “Things fall because of gravity, and rise because of levity.” Or Molière’s virtus dormitiva. But more may be packed into such terms
than may be initially apparent.
As, one philosopher pointed out that “The ball rebounded to the height
that it did because of its resiliency.” But this is informative: the height is owing to internal characteristics of that
ball, rather than from the ball’s having been dropped from a greater height, or
having been dropped on a more resilient surface.
Additionally, the initial tautological character of a
sentence can so to speak “age off”, in accordance with semantic
evolution of its terms. Thus, “Atoms are indivisible” was initially as circular
as “Bachelors are unmarried”, since they were defined from the outset as indivisibilia (as their name, a-tom, etymologically implies). But on its current interpretation, the
sentence would qualify as false.
A mathematician looks at Newton’s Definition 1, in the Principia:
Quantity of matter is a measure of matter that arises from its
density and volume jointly.
Great acumen is hardly needed to
realize that this definition is hopelessly circular, since density is normally
defined as the ration of mass to volume;
but Newton’s unhelpful phrase
does have some implicit implications. For example, we expect the mass of an object to remain
unchanged if we change its shape.
-- Michael Spivak, Physics for
Mathematicians: Mechanics I (2010), p. 9
~
A 2015 example
of the uses of tautology:
Robert Buissière on Médi1, re Presidential candidates:
Jeb Bush, frère de son frère,
et Hillary Clinton, épouse de son époux.
As they stand, these are statements “analytic”; but we
understand the import: Jeb and
Hillary got where they are today, largely owing to family association.
Cf. & contrast the common expression “He is his father’s
son.” Normally this means that he
takes after his Dad, and not that he is getting any special favors from other
people owing to that filiation. To
imply the latter, you might say “Daddy’s little boy” or something. By contrast, the French phrases in the
above context do not imply that
Jeb’s politics are a close match to Dubya’s, let alone that Hillary’s are a
close match to Bill’s.
~
A bare tautology like “Business is business”, as a free-standing
statement, invite contentful interpretation via a “Gricean implicature”
(specifically, the Maxim of Quantity). The following is a syntactically more complex case,
there the tautology is embedded in a subordinate clause:
Ever since self was self, nature
been keepin’ folks off of red-hot stoves.
-- Zora Neale Hurston, Their
Eyes Were Watching God (1937)
The meaning is:
Common sense has been extant
from time immemorial.
Operationally, the (tongue-in-cheek) interpretation is: Go back and back in time, sampling as
you go. For each sample-point, verify whether “self = self” holds at that time; and if so, then evaluate “Common
Sense is in effect? Y/N”. The
sentence, for all its folksiness, has a kind of philosophy-class spin to it;
the moreso as “self = self” calls up First-Order Logic with Identity.
~
Stylistic
appreciation
Usually there is a summary “That’s that” finality to tautologies, whether used informatively or
not; stylistically, they are
bare-bones. But consider this:
Herod: The moon has a strange look tonight. … She reels through the
clouds like a drunken woman. … Does she not reel like a drunken woman? She is like a madwoman, is she not?
Herodias: No; the moon is
like the moon, that is all.
-- Oscar Wilde, Salomé
(1891)
Here the barrenness of the pale white, plain round far-floating body, is reflected in the
unyielding tautological formula.
~
Enten-Eller
Philosophers
have scribbled much ink, and later worn out many a typewriter ribbon, and
finally expended great bushels of pixels, discoursing upon the status of “logical
truths”; such as, paradigmatically, the following:
(I) Every man is either married or a bachelor.
(We
simplify, since the matter is not really of interest; leaving out of account,
for instance, the curious case of Schrödinger’s
groom.)
It
is agreed that such a sentence tells us nothing about the world, unlike that
time-honored exemplar of informativeness,
(II) The cat is on the mat.
which
has been so oft repeated. down the years, that said cat has achieved the
immobility and timelessness of an Egyptian idol. (Presumably the mat lies in a patch of sunlight, so why ever
move?)
And yet its affordances are quite different from those of another statement of
the same logical form; say:
(II) Every number is either even or odd.
For,
although the sentence (I) does not perhaps baldly state anything substantive about the world, its presuppositions
speak volumes. For one thing, it gives us to understand that there is a
sharply defined institution, Marriage, into which a man may enter or not; and
that his resultant state is either-or. Even so much will give our Martian
anthropologists sufficient grist for many turns of the mill.
~
The
above are mostly individual linguistic parlor-tricks. Much more generally, there is the matter of the status of
the equations of mathematics. A
view put forward by the dessicated and ennervating tendency called formalist
nominalist maintained that, being
mathematical, they are tautologies, and being tautologies, they are
uninformative -- semantically vacuous.
Practical experience shows that doctrine to be false. As a way to see how such equations
manage to be informative, consider the number pi.
Pi
can be defined, qualitatively, in a number of diferent ways, most familiarly as
the ratio of a circle’s circumference to is diameter. It is,
moreover, a Given of the invisibilia,
woven into the fabric of the noöspheric pattern; and -- crucially -- it can be reacher in a startling variety
of precise quantitative ways, along this strand or that of the warp and the
woof -- and the woorp and the wahf, along any of the dimensions of the
multidimensional mathematical textile. Pi is itself ever one, the peak of the Golden
Mountain; but the paths that climb
to it are numberless. It can be
expressed as a definite integral; as an infinite continued fraction; as an
infinite product; as an infinite sum; with many variations of each. (Behold some of them at https://en.wikipedia.org/wiki/Pi.) That fact that any one of these equals π is informative and indeed amazing, for in
effect each one constitutes hiking instructions -- a trail-map -- to the
summit, each from a wildly different base-camp. And each one of these infinitely intricate expressions is equal to any other, in an equation
which is as distant from tautological or uninformative as can be imagined.
~
[Update
13 May 2020] An aborbing article
by Evan Osnos, in the 11 May 2020 issue of The New Yorker, maps out the
paths by which the Greenwich Connecticut
tennis-and-boating-club crowd
came to support Trump. The notables
of that town have a patrician heritage, in principle at variance with the flashy
style of the vulgarian from the Bronx, but as one blue-blood testifies, his
conversion came while witnessing an early speech by the candidate: “He had that line that he would use: ‘Folks,
we either have a country or we don’t.’
And I felt the chill .. I’m, like, ‘Oh, my God, this is a really good line.’
Apart
from the formally tautological character of that line, it puzzles by its
vagueness: out of context, it is
unclear what at all is being hinted at.
Presumably the line is a dog-whistle, a bit of Rorschach rhetoric from
which the listener will extract whatever meaning he likes.
The
line does nothing for me; but it does recall such successful political
antecedents as “The business of America is business.”
~
[Update
14 May 2020]
Some
of you may be familiar with the British sport of trainspotting. That
may or may not be in accordance with current U.K. guidance on coronavirus
lockdown. But here’s a hobby you
can practice in the safety and comfort of your own home:
Tautology-Spotting
!
As:
Headline
in this morning’s New York Times:
The
People Behind the Counter Are People
Remember this the next time you order takeout.
That
one recalls those sleep-inducing example-sentences from introductory logic
class (All brave Athenians are Athenians). But in this case, it has a punch, and the source of that
punch is not logical but lexical.
For, people has a variety of
senses; from the neutrally
classificatory
(a)
an instantiation of the species Homo
sapiens, near-cousin of Pan
troglodytes, sometimes known as “a forked radish”;
to
the “pregnant sense” (I phrase it
freely)
(b)
an ensouled being created in the image of the Lord of Hosts, whom Christ
died to redeem.
In
the cited sentence, the first occurrence of the word people has the (a) meaning; the second occurrence, (b).
For
more on perspectival semantics and pregnant senses, check out this essay:
~
In
all the instances above, tautology is
used in its traditional logico-philosophical sense. But technical terms sometimes get picked up by a wider
audience, where their use may be lax.
Thus, the literary critic V.S. Pritchett, in his article on the novelist
Anthony Powell, wrote:
Mr. Powell is excellent with the raffish….
I think the sententious irony succeeds. … It adds a very English flavor, either
of comic tautology or deflation.
The
sense of tautology is unclear here. Perhaps it refers to mechanical repetition, a standard
component of broad humor.
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