Download Hausa Grammar and Classical Logic: Transculturality of Sentential

Metalogicon (2004) XVII, 2
Hausa Grammar and Classical Logic:
Transculturality of Sentential Calculus
Nunzia D’Aniello
ABBREVIATIONS
AC.P. = ACTUALISATION PARTICLE
ADJ. = ADJECTIVE
ADV. = ADVERB
AO. = AORIST
A.P. = ATTACHMENT PARTICLE
ART. = ARTICLE
C.A. = COMPLETED ASPECT
CONJ. = CONJUNCTION
F.N. = FEMININE NOUN
F.V. = FUTURE VERB
IMP.V. = IMPERATIVE VERB
IND.ADJ. = INDEFINITE ADJECTIVE
INF.V. = INFINITIVE VERB
M.N. = MASCULINE NOUN
N.P. = NEGATIVE PARTICLE
P.A. = PARTITIVE ADJECTIVE
P.C. = PERSONAL CONTINUATIVE
P.N. = PERSONAL NOUN
P.P. = PRESENT PARTICIPLE
P.PRON. = PERSONAL PRONOU
PL. = PLURAL
PREP. = PREPOSITION
PRE.SUBJ. = PRESENT SUBJUNCTIVE
PRE.IND. = PRESENT INDICATIVE
P.T. = PAST SIMPLE TENSE
R.P. = RELATIVE PRONOUN
S. = SUBSTANTIVE
U.A. = UNCOMPLETED ASPECT
V. = VERB
1. Hausa grammatical characteristics
The Hausa language, which is spoken in centre-west
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Metalogicon (2004) XVII, 2
Africa, presents many grammatical aspects which make it very
different from the Indo-European languages.
First of all, in Hausa, the verb «to be» does not exist, so it
is expressed by the enclitic actualization particles: ne , ce . The
first one is used after a singular or plural masculine noun, the
second one after a singular or plural feminine noun.
See the example below:
It
is
a
city
P.PRON.
PRE.IND.
ART.
S.
In Hausa:
gari
ne
M.N.
AC.P.
Literally: City is
In Hausa the genitive is expressed by three suffixes called
«attachment particles», which take place of the English «of». They
are –n for masculine, -r for feminine, -n for plural. See the
following instance:
The
horse
of
the
chief
ART.
S.
PREP.
ART.
S.
In Hausa
Doki–n
sarki
M.N. – A.P. M.N.
Literally: Horse–belonging to chief. (‘–n’ is an attachment
particle concerning the following noun).
In the western languages, like Italian, German, French, verb
is inflected in moods and tenses, which means that there is a
temporal system. In Hausa, on the contrary, tense is something
secondary, because verb expresses time but only to determine the
expression it is referred to. In fact, the verbal system is figurative
and what is important is the kind of action expressed by the verb.
Consequently, action can be completed or uncompleted, as
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Metalogicon (2004) XVII, 2
we notice in the following examples:
I
ate
some
meat
P.PRON.
P.T.
P.A.
S.
In Hausa:
Na
ci
nama
P.PRON.
C.A.V.
F.N.
Literally: I to eat (verb in the completed aspect) meat.
This language, therefore, presents some features which
make it different from the western ones, but it is no wonder if we
think that in the whole world there is a large variety of different
languages with regard to their structures and syntaxes.
So the question is: does the formal logic have an exclusive
relation with a particular language or a group of languages, or has
it something to do with language itself?
The classical logic is characterised by bivalence, no
temporality, inter-definable connectives, acceptation of the third
excluded law, etc. Hence the question arises: does it innervate all
the languages or just the Indo-European shackle which has
conceived it?
As there is an inseparable relation between mind and
language, the question now is: does the learning of a language go
together with the learning of a new logic?
On this subject, it is interesting to compare the main points
of the classical logic to the Hausa, a tonal language, whose syntax
and phonetics are very different from that of the Indo-European
languages which elaborated the formal logic.
The Hausa language belongs to the Chadic group of the
Afro-Asiatic family of languages, and it is spoken in a large area
of sub-Saharan Africa, which includes the countries of Niger,
Nigeria and Chad. It has been classified as a Semitic language
(like Arabic, Hebrew, Aramaic, etc.), and it is closely related with
Berber, ancient Egyptian and the Cushitic languages. This is
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Greenberg’s classification [GREENBERG (1963)]. It has gained
general acceptance.
Till first decades of the last century, Hausa was written in
Arabic characters, the Ajami. In 1911, Hans Visher, a Swiss
scholar, English by adoption, made the first important study about
the way Hausa could be written in Latin characters [VISHER
(1911)] and his essay was supported by the English monarchy,
which improved the diffusion of this new writing system. This
involved the necessity, for the Europeans, of an understandable
graphic system relating to a standard language which had to be
chosen among the great variety of the Hausa dialects. The Kano
dialect seemed to be the most appropriate, unless when it was
completely different from the other ones.
In Hausa, as we said before, one of the most pregnant
grammatical feature is the fact that the verb «to be» does not exist,
therefore it is expressed by the actualisation particle. See the
examples below:
1st instance:
It
is
a
horse
P.PRON.
PRE.IND.
ART.
S.
In Hausa:
Doki
ne
M.N.
AC.P.
Literally: Horse is.
2nd instance
It
is
a
road
P.PRON.
PRE.IND.
ART.
S.
In Hausa:
kanya
ce
F.N.
AC.P.
Literally: Road is.
3rd instance
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Metalogicon (2004) XVII, 2
They
are
some
goats
P.PRON
PRE.IND.
P.A.
S.PL.
In Hausa:
Awaki
ne
M.N.PL.
AC.P.
Literally: Goats are
In Hausa, the verb «to have» does not exist, so it is
expressed by the person of the uncompleted aspect construction
plus «da», as in the following example:
I
have
money
P.PRON.
PRE.IND.
S.
Ina
da
kudi
P.PRON.
V.
M.N.
In Hausa:
Literally: I to have money. ‘Ina’ is the first personal continuative
person-aspect construction.
The verbal system, as we said before, is one of the most
complex aspects of the Hausa grammar because it depends on the
action, which can be completed or uncompleted [See KRAFT,
KIRK-GREENE (1973) p. 145]; besides, it presents a very typical
verbal tense, the Aorist, or subjunctive, which is used to express a
not indefinite action [See BALDI (1992) p. 25].
These verbal aspects have their equivalence in the classical
terminology:
COMPLETED ASPECT
PERFECT, PAST, PERFECTIVE.
UNCOMPLETED ASPECT IMPERFECTIVE,
PRESENT,
PROGRESSIVE CONTINUOUS.
AORIST
SUBJUNCTIVE
See the examples below:
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Metalogicon (2004) XVII, 2
1st instance
You
ate
some
meat
P.PRON.
P.T.
P.A.
S.
In Hausa:
Ka
ci
nama
P.PRON.
C.A.
M.N.
Literally: You to eat meat. ‘Ka’is the second singular masculine
completive person- aspect pronoun.
2nd instance
I
am
coming
P.PRON.
PRE.IND.
P.P.
In Hausa:
Ina
P.PRON.
zuwa
U.A.
Literally: I to come (uncompleted aspect)
3rd instance
Let
me
come
IMP.V.
P.PRON.
INF.V.
In Hausa:
In
P.PRON.
zo
V.
Literally: (That) I come (Aorist. form). ‘In’ is the first singular
subjunctive person-aspect pronoun.
In Hausa, there are two future aspects. The Future I
expresses an action which has already started, by employing the
specialized verbal za plus the subjunctive aspect person-aspect
pronouns. The Future II expresses an uncertain and indefinite
action [ See GOUFFÉ (1965) pp. 191-210].
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See the examples below:
Future I
1st instance
Men
will leave
S.PL.
F.V.
In Hausa:
Mutane
za
PL.N.
su
tafi
P.PRON.
V.
Literally: “Men they leave”. Note that ‘za’ is used with personal
pronoun to express the Future I.
2nd instance
I
will come
P.PRON.
F.V.
In Hausa:
Na
zo
V.
Literally: “I to come” (Future II aspect). ‘Na’ is the first singular
Future II person-aspect pronoun.
As we have noticed, while in the Indo-European languages,
time is expressed by changes in the verb itself, in Hausa it is
expressed by changes in the personal pronoun. For example, the
sentence «I’m coming», in Hausa will be «ina zuwa», where the
pronoun «ina» introduces the continuative or uncompleted
construction. This means that in Hausa, temporality is expressed
by the variation of the pronoun.
A question arises: Given such different grammatical frames
are we allowed to speak of transculturality of classical sentential
logic?
2. Logical connectives
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We will examine the presence and use of the logical
connectives in Hausa starting from the negative sentence. This is a
molecular utterance born by negation of an atomic sentence.
The negative, in Hausa, is formed by placing two particles:
«ba.......ba», which delimit what is denied.
In this respect, it is interesting to see how negative in
Hausa is similar to the French negative «ne… pas». Let the
following atomic sentence be:
It
is
him
P.PRON.
PRE.IND.
P.PRON.
In Hausa:
Shi
ne
P.PRON.
AC.P.
Literally: “He is”.
The negation of the above sentence is:
It
is
not
him
P.PRON.
PRE.IND.
ADV.
P.PRON.
In Hausa:
ba
shi
ne
ba
N.P.
P.PRON.
AC.P.
N.P.
Literally: Not he is not.
Starting from these examples, we can sketch the below table,
where GASKIYA and KARYA translate English TRUE and
FALSE respectively :
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Metalogicon (2004) XVII, 2
Shi ne
GASKIYA
KARYA
Ba shi ne ba
KARYA
GASKIYA
Let symbolise “Shi ne” by ‘p’ and “Ba shi ne ba” by ‘Np’ we
obtain the following table of classical logic negation where ‘N’ is
the negation function in Polish symbolic language. We have
p
1
0
Np
0
1
Now, we will go on analysing the logical product, or
copulative.
As we know, the classical logic has only two truth values:
true and false, hence, when we have two atomic sentences, the
corresponding possibilities or dispositions are four: both are true;
the first is true and the second is false; the first is false an the
second is true; both are false. The truth values of molecular
sentences generated by the logical functions are therefore four. Let
us begin with the logical product.
In Hausa, the conjunction «and» is expressed by the
particle «da». Let us consider two atomic sentences, for example
«it is raining» and «the wind is blowing». The Hausa
corresponding ones are “ana yin ruwa” (literally: it makes rain)
and “ana yin iska” (literally: it makes wind). To the English
molecular sentence “it is raining and the wind is blowing”
corresponds the Hausa “ana yin ruwa da iska” (literally: it makes
rain and wind), simplified expression for “ana yin ruwa da ana
yin iska” (literally: it makes rain and it makes wind). Now let us
sketch the truth table of logical product:
ana yin ruwa
GASKIYA
GASKIYA
KARYA
KARYA
ana yin iska
GASKIYA
KARYA
GASKIYA
KARYA
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ana yin ruwa da iska
GASKIYA
KARYA
KARYA
KARYA
Metalogicon (2004) XVII, 2
Now if we symbolise “ana yin ruwa” by ‘p’, “ana yin iska” by ‘q’,
“ana yin ruwa da iska” by ‘Kpq’ like in Polish symbolism, we
obtain the classical truth table of logical product
p
1
1
0
0
q
1
0
1
0
Kpq
1
0
0
0
As we can notice, the truth table is the same of the Indo-European
languages.
The examples given till now have shown the use of some
connectives in the Hausa language, so now we will consider the
use of the connective «or», one of the few words of everyday life
which has so much linguistic ambiguity. In Hausa it is expressed
by the word «ko».
See the example below:
It is raining or the wind is blowing
In Hausa we have:
Ana yin ruwa ko iska
Literally: It makes rain and wind.
In this example, «Ana yin ruwa ko iska» is a molecular
utterance composed by two atomic utterances: «Ana yin ruwa»
and «Ana yin iska». The verb «yin», which means «to do», takes
both the nouns «rain», «ruwa», and «wind», «iska». The two
atomic utterances are linked by the connective «ko». In the above
example the connective «ko» has an inclusive meaning because
both utterances are compatible and they might also take place
together. In this case, the connective «ko» can be compared to the
Latin «vel». [On this interesting topic see MALATESTA (2003)].
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Now, we will calculate the logical sum by using Hausa both
as language and metalanguage , we obtain the following table:
ana yin ruwa
GASKIYA
GASKIYA
KARYA
KARYA
ana yin iska
GASKIYA
KARYA
GASKIYA
KARYA
ana yin ruwa ko iska
GASKIYA
GASKIYA
GASKIYA
KARYA
Symbolising «ana yin ruwa» by ‘p’, «ana yin iska» by ‘q’ and
«Ana yin ruwa ko iska» by ‘Apq’like in Polish symbolism, we
obtain the following truth table which proves the transculturality
of logical function of inclusive disjunction.
p
1
1
0
0
q
1
0
1
0
Apq
1
1
1
0
In logic, the Hausa connective «ko» («or») can be also used
except when the two utterances are both possible but they can’t
take place together.
See the example below:
.
Is it day or night
In Hausa:
Rama ne ko dare
Literally: Day is or night.
As you can see such a molecular sentence is a contracted
form of the following expression «rama ne ko dare ne», which is
made up two atomic sentences «rama ne» and «dare ne». In this
case, the connective «ko» expresses the meaning of the Latin
«aut».
Now we will write the exclusive sentence using Hausa
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language both as language (in italic) and metalanguage (in capital
letters).
rama ne
GASKIYA
GASKIYA
KARYA
KARYA
dare ne
GASKIYA
KARYA
GASKIYA
KARYA
rama ne ko dare
KARYA
GASKIYA
GASKIYA
KARYA
Now if we symbolise “rama ne” by ‘p’, “dare ne” by ‘q’, “rama
ne ko dare” by ‘Jpq’ as in Polish symbolism, we obtain the truth
table of exclusive disjunction:
p
1
1
0
0
q
1
0
1
0
Jpq
0
1
1
0
In logic, another meaning of the connective «or» is that of
the incompatibility, since either the first utterance or the second is
possible or neither of them.
See the example below:
The team of Nigeria wins or loses
contracted form of the molecular sentence «The team of Nigeria
wins or the team of Nigeria loses», made up of two atomic
sentences «The team of Nigeria wins» and «the team of Nigeria
loses», connected by «or» in the meaning of «nand». [See
MALATESTA (1997), pp. 86-93].
In Hausa:
kungiya Nigeriya yaa ci ko an ci sa
Literally: The team of Nigeria has won or has been won (or
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defeated). Also such a molecular sentence is a contracted form of
the following expression «kungiya Nigeriya yaa ci ko kungiya
Nigeriya an ci sa», which is made up two atomic sentences
«kungiya Nigeriya yaa ci», and ««kungiya Nigeriya an ci sa». In
this case, the connective «ko» expresses the meaning of «the first
is true, or the second is true, or both are false». Therefore the case
that both are true is excluded. Hence the name «nand» = «not
and» given to such a logical function. In this example, it’s evident
that there is no likelihood of the victory and defeat of the Nigerian
team at the same time, but there are three possibilities: the
Nigerian team could win, lose or draw. The meaning of the
connective «or», in this example, is that of the incompatibility:
one or another, or neither of them.
See the informal Truth table below in Hausa language.
kungiya
Nigeriya yaa ci
GASKIYA
GASKIYA
KARYA
KARYA
kungiya
Nigeriya an ci
sa
GASKIYA
KARYA
GASKIYA
KARYA
kungiya Nigeriya yaa ci
ko an ci sa
KARYA
GASKIYA
GASKIYA
GASKIYA
Symbolising “kungiya Nigeriya yaa ci” by ‘p’, “kungiya Nigeriya
an ci sa” by ‘q’, “kungiya Nigeriya yaa ci ko an ci sa” by ‘Dpq’ as
in Polish symbolism, we obtain the truth table of exclusive
disjunction of classical logic:
p
1
1
0
0
q
1
0
1
0
Dpq
0
1
1
1
Now we will examine the material implication, which is the
most basic logical function because it does not include an
additional significance to the original one. Its meaning is:
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Metalogicon (2004) XVII, 2
Cpq =df NKpNq
In the Hausa language, the connective «if....then» is expressed
by: « idan …sa’an». See the example below:
if it raining then the wind is blowing
In Hausa:
idan ana yin ruwa sa’an iska
Literally: If it makes rain, then (it makes) wind. See the following
table where Hausa is used both as object language and
metalanguage. As far as the material implication is concerned see
the important experiment made in Zambia in MALATESTA (2003).
ana yin ruwa
ana yin iska
GASKIYA
GASKIYA
KARYA
KARYA
GASKIYA
KARYA
GASKIYA
KARYA
idan ana yin ruwa
sa’an iska
GASKIYA
KARYA
GASKIYA
GASKIYA
Let ‘p’ stand for “ana yin ruwa”, ‘q’ for “ana yin iska” and
‘Cpq’ for “idan ana yin ruwa sa’an iska”, contracted form for
“idan ana yin ruwa sa’ana ana yin iska”. The above table can be
symbolised as follows:
p
1
1
0
0
q
1
0
1
0
Cpq
1
0
1
1
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Metalogicon (2004) XVII, 2
Once again we can note the transculturality of sentence classical
logic.
Now shall analyse the material equivalence, which can be
derived from the material implication. Do not forget the classical
standard definition
Epq =df KCpqCqp
The above connective, which in English is expressed by the phrase
«if only if», in the Hausa language becomes «idan kadai idan».
See the example below:
if it raining if and only if the wind is blowing
In Hausa:
ana yin ruwa idan kadai idan iska
Literally: If it makes rain if only if (it makes) wind.
See the table below:
ana yin ruwa
ana yin iska
GASKIYA
GASKIYA
KARYA
KARYA
GASKIYA
KARYA
GASKIYA
KARYA
ana yin ruwa idan
kadai idan iska
GASKIYA
KARYA
KARYA
GASKIYA
Now if we symbolise “ana yin ruwa” by ‘p’, “ana yin iska” by ‘q’
and ‘Epq’ for “idan ana yin ruwa sa’an iska”, contracted form for
“ ana yin ruwa idan kadai idan ana yin iska”, the above table
becomes
p
1
1
0
q
1
0
1
Epq
1
0
0
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Metalogicon (2004) XVII, 2
0
0
1
3. Conclusion
Our study has showen that the grammatical structure of the
Hausa language has some specific features which make it very
different from the west languages, but it is possible to say that the
formal logic does not favour an exclusive relation with a language
or a group or languages, because it has something to do with
language itself.
It is common knowledge that there is an inseparable relation
between mind and language, but the learning of a new language
does not mean that we learn also a new logic.
The fact that we talk about the logic of the Italian or Chinese
language hides an ambiguity of language. In this case, the Chinese
logic means the keeping of its grammar structures. In the Latin
language, for example, when a text has three if clauses, we are in
the presence of the Latin logic, actually the Latin logic is the
keeping of its grammar rules. But logic means the science of the
necessary inferences and of the conditions which make it possible.
These conditions are given by the connectives and their respective
True-False tables.
Consequently, if the morphologic structures of a Chadic
language of the Afro-Asiatic family like Hausa have the same
logical functions of the west languages, it’s clear that we are in the
presence of one and only one logic.
Even though grammars are often different from one another,
there are some elements which join together the languages of the
whole world, and they are represented by the logical functions.
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