Logico-Semantical Analysis of Natural Language Expressions is not

Transkript

Logico-Semantical Analysis of Natural Language
Expressions is not a Translation
Logika: systémový rámec rozvoje oboru v ČR a koncepce logických propedeutik
pro mezioborová studia (reg. č. CZ.1.07/2.2.00/28.0216, OPVK)
doc. PhDr. Jiří Raclavský, Ph.D. ([email protected])
Department of Philosophy, Masaryk University, Brno
Jiří Raclavský (2014): Logical-Analysis of Natural language Expressions is not a Translation
1
Abstract
It is sometimes assumed that logico-semantical analysis of natural language consists in translation of natural
language expressions into formal language ones. A moment reflection reveals that this translational thesis has
unacceptable consequences. Firstly, to explain the meaning of the formal expression which is a translation of a
natural language expression, one has to translate it into another language, thus an infinite regress of translations
arises. Secondly, the translation does not disclose the meaning (it indicates only the sameness of meanings),
which is a serious drawback because the semanticist's aim is to explicate meanings. In addition to a criticism of
that translational thesis, I offer an alternative explanation of typical findings of semanticists (written
juxtapositions of natural and formal expressions) which fits the idea that logico-semantical analysis of natural
language should provide 〈expression, meaning〉 pairs.
Logika: systémový rámec rozvoje oboru v ČR a koncepce logických propedeutik pro mezioborová studia (reg. č. CZ.1.07/2.2.00/28.0216, OPVK)
2
Content
I.
Against Translational thesis
II. Logical analysis of analysts’ sentence
III. Explicative / investigated language
IV. Conclusions
3
I. Against Trans
Translational
nslational thesis
4
I. Aims of LANL
- the very presupposition of semantics, logical analysis, of natural language (LANL
LANL)
LANL is
that expressions of natural language NL have meanings
- the very aim of LANL is to explicate (in Carnap’s sense) these meanings, i.e. model
them by means of rigorous tools (e.g., “logic”)
5
I. PrePre-theoretical / theoretical knowledge of meaning
- analyst (semanticist) understands the expressions of NL, grasps their meanings,
already pre-theoretically;
- but analyst does more when offering their theoretical explicans
- compare with knowing how to ride a bike and a physicist explaining which laws
and powers are necessary to ride a bike
6
I. Analytician’s sentence (AS)
AS):
- a typical result achieved by an analyst takes form of analyst’s sentence (AS
AS
“The meaning of the expression ‘E’ (in NL) is ϕ.”
− whereas “ϕ” is a formula of some formal language FL
− AS is stated in the NL enriched by FL, i.e. in NFL
- a particular AS delivers certain message (about meaning of “E”) to other analysts,
thus it must be meaningful
- a particular AS is considered (by another analyst) true or false, thus it must be
meaningful first
7
I. Translational thesis (TT)
- “E2” (of L2) is a translation of “E1” (of L1) iff the meaning of “E2” in L2 is the same as the
meaning of “E1” in L1
- translational thesis (TT
TT):
TT
LANL consists in translation of NL expressions onto expressions of FL
(or: analyst translates “non-transparent” part of NFL, i.e. NL, to “transparent” part
of NFL, i.e. FL; TT has been recently defended by Peregrin 1993)
8
I. An argument for TT?
- meanings are extra-linguistic entities, thus one cannot put, side-by-side,
expressions with their meanings into her/his findings
- the above reason is not compelling for an objector to TT:
− in order to direct the attention of an audience to certain meaning, s/he must use
some expression (say “ϕ” of FL)
− yet TT does not follows from it
9
I. Undesirable consequences of TT
- to say that the meaning of “E2” in L2 is the same as the meaning of “E1” in L1 (i.e. that “E2”
is a translation of “E1”) left the meaning of “E1” (in L1) entirely unexamined
- the identity claim (stating in fact the inter-translatability of two expressions)
provides no explication of the (of “E1”), no theoretic model of “E1’’s meaning is
offered
- to know that the meaning of “E1” in L1 is the same as the meaning of “E2” in L2 does
not amount to know what exactly is the meaning of “E1” (in L1)
10
I. Undesirable consequences of TT (continuation)
- the problem was only shifted elsewhere, namely from L1 to L2
- one must then ask: what is the meaning of “E2”?
- answer: the meaning of “E2” (in L2) is the same as the meaning of “E3” (in L3)
− it has, however, an undesirable consequence: an infinite regress of translations
- therefore: unless LANL is quite idle, TT must be rejected
11
I. What remains to explain?
explain?
- what remains to explain or elaborate:
a. to provide the logical analysis of AS (especially, to explicate the meaning of “ϕ”
in NFL)
b. to explain what is the role of FL’s expressions in NFL (why FL’s expressions are
not intertranslatable with NL’s expressions)
c. to explain why it possible to capture the meaning FL’s expressions in FL and then
use FL for explication of meanings of NL
12
II. Logical analysis of analysts’
analysts’ sentence
13
II. Transparent Intensional Logic - semantic scheme
- semantic scheme:
an expression
E expresses (means):
a construction
E denotes (names):
C constructs:
a denotatum
“E”
|
C
|
|
D (intension / non-intension)
- constructions are structured procedures (Tichý 1988, 2004)
- constructions are usually recorded by means of certain λ-terms
14
II. Example of logical analysis
− the expression “2+3”
expresses:
|
[0+ 02 03]
denotes:
(a construction of the number 5)
|
5
− the expression “Xenia computes 2+3” expresses (in English) the construction of the
denoted proposition:
λwλt [0Computewt 0Xenia 0[0+ 02 03] ]
− the trivialization 0[0+ 02 03] constructs the construction [0+ 02 03], not the number 5
constructed by [0+ 02 03]
15
II. The logical analysis of AS
“The meaning of the expression ‘Xenakis is a composer’ (in English)
is the construction λwλt [0Composerwt 0Xenakis]”
expresses (in English) the construction:
λwλt [0MeaningOf 0“Xenakis is a composer”
0
[ λwλt [0Composerwt 0Xenakis]] ]
- 0
“Xenakis is a composer” constructs a Gödelian number; 0[λwλt [0Composerwt
0
Xenakis]] constructs the construction λwλt [0Composerwt 0Xenakis]; 0MeaningOf
constructs a relation between numbers-expressions and constructions
- language (English) must also be explicated (see e.g. JR 2012) and incorporated into the analysis
16
II. Why AS does not exhibit a translation
- within NFL:
“Xenakis is a composer”
|
“λwλt [0Composerwt 0Xenakis”
|
expresses:
λwλt [0Composerwt 0Xenakis]
|
that proposition
denotes:
0
[λwλt [0Composerwt 0Xenakis]]
|
λwλt [0Composerwt 0Xenakis]
- clearly: “E” expresses (means) certain construction C,
while “ϕ” expresses (means) the construction-trivialization 0C
- the meanings of “E” and “ϕ” radically differs, thus they are not intertranslatable at all
17
II. Tichý on translatability
- in his unpublished monograph Introduction to Intensional Logic (1976), and also in
print Tichý writes:
“we use the [TIL] formula to name [i.e. to denote] the construction which ... is expressed (not
named! [i.e. not denoted]) by the English sentence.”
(Tichý 1980: 352)
“By juxtaposing a formula in that [TIL] notation with an English sentence ... we do not offer
the formula as a translation of that sentence”
(Tichý 1980: 352)
- however, within the simple type-theoretic framework Tichý could not fully explain
the matter (he could not provide the logical analysis of AS)
- only ramified type-theoretic framework enables us to adequately show the lack of
intertranslability of those expressions (and also properly analyze the analyst’s
sentence) due to the explicit treatment of constructions within the framework
18
II. Montagovians
Montagovians on translatability
- Montague (1974) and his followers repeatedly speak about translation of natural
language expressions in the language of Montague’s Intensional Logic (IL),
suggesting thus that 〈natural language expression, IL-term〉 pairs have the same
model-theoretic meaning (as it is known, IL lacks a hyperintensional level, which is
its deficiency)
- on the other hand, some Montagovians have already conceded that they need not
provide real translations:
“Intensional Logic [serves] as a formalized part of our metalanguage’, whereas our
metalanguage contains also ‘ways of referring to object language (e.g., English)”
“Intensional Logic could provide us with names for meanings’ of expressions of the object
language − thus Montague’s method of translations is not necessary”
(Dowty, Peters, Wall 1992: 264)
19
20
III. Conceptual role of FL’s
FL’s expressions in NFL
- the role FL’s expressions in NFL is conceptual, not usual
- FL’s expressions are meaningful in NFL only in the supposition conceptualis:
“the (construction) λwλt.λx [0Canitywt x] is a construction of the kind closure”
while being nonsensical in the supposition usualis:
“the (property) λwλt.λx [0Canitywt x] is instantiated by Fido”
21
III. Conceptual role of FL’s
FL’s expressions in NFL (continuation)
- NL’s expressions are nonsensical in NFL in the supposition conceptualis:
“the (construction) canity is a construction of the kind closure”
while being meaningful in the supposition usualis:
“the (property) canity is instantiated by Fido”
- this shows a deep incommensurability of semantical features of NL’s and FL’s
expressions
- in sequel, there is no surprise that they are not intertranslatable
22
- when doing LANL, NL such as (ordinary) English is an investigated language
- it is investigated by means of the explicative language such as the “language of
constructions”
- when an explicative language becomes embedded in the investigated language, the
expressions of the explicative language become to serve as a conceptual tool, thus
they are meaningful, in the investigated language, only in the supposition
conceptualis
23
III. Explicative / investigated language (continuation)
- when the formal explicative language (e.g. λ-calculus) was introduced to us, the
semantics of its expressions was characterized by means of English which served
on this occasion as the explicative language for the investigation of the formal
language
- the roles has swapped when the formal explicative language become to be the
explicative language for English
- realize that Tarski’s (1956) object language / meta-language treats a distinct
phenomenon (!)
24
IV. Conclusions
25
IV. Conclusions
- the meanings of the natural language expression “E” and its logical analysis “ϕ”
(within enriched natural language) radically differs, thus they are not
intertranslatable at all
- the logical analysis of sentences “The meaning of ‘E’ is ϕ” can be provided in the
late TIL which utilizes ramified theory of types
- we have exposed also other reasons showing that Translational thesis (claiming
that analysts translate “E”s onto “ϕ”s) is false
- analyst analyzing a language L treats it as an investigated language and describes it
within an explicative language
26
Key references
Raclavský, J. (2010): Is Logical Analysis of Natural Language a Translation?. In: P.
Stalmaszczyk (ed.), Philosophy of Language and Linguistics Volume I: The Formal Turn,
Frankfurt am Main: Ontos Verlag, 229-243.
27
References
Dowty, D.R., Wall, R.E., Peters, S. (1992): Introduction to Montague Semantics. Dordrecht: Kluwer.
Montague, R. (1974): The Proper Treatment of Quantification in Ordinary English. In: Formal Philosophy, New Haven, London: Yale University
Publisher, 247-270.
Peregrin, J. (1993): Is Language a Code?. The Logical Point of View 2, 73-79.
Raclavský, J. (2010): Is Logical Analysis of Natural Language a Translation?. In: P. Stalmaszczyk (ed.), Philosophy of Language and Linguistics
Volume I: The Formal Turn, Frankfurt am Main: Ontos Verlag, 229-243.
Raclavský, J. (2012): Základy explikace sémantických pojmů. Organon F, 19, 4, 488-505.
Raclavský, J. (2014): A Model of Language in a Synchronic and Diachronic Sense. In print.
Tarski, A. (1956): The Concept of Truth in Formalized Languages. In: Logic, Semantics and Metamathematics, Oxford University Press, 152-278.
Tichý, P. (1980): The Logic of Temporal Discourse. Linguistics and Philosophy 3, 373-369.
Tichý, P. (1988): The Foundations of Frege’s Logic. Berlin, New York: Walter de Gruyter.
Tichý, P. (1992): The Scandal of Linguistics. From the Logical Point of View 1, 70-80.
Tichý, P. (1994): Cracking the Natural Language Code. From the Logical Point of View 3, 6-19.
Tichý, P. (1994a): The Analysis of Natural Language. From the Logical Point of View 3, 42-80.
Tichý, P. (1988): The Foundations of Frege’s Logic. Walter de Gruyter.
Tichý, P. (2004): Pavel Tichý’s Collected Papers in Logic and Philosophy. V. Svoboda, B. Jespersen, C. Cheyne (eds.), University of Otago Press,
Filosofia.

Logico-Semantical Analysis of Natural Language Expressions is not

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