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Topic-focusTopic-focus ambiguities ambiguities in natural languagein natural languageMarie DužíMarie DužíVSB-Technical University Ostrava & Charles University of PragueMarie.duzi@vsb.cz http://www.cs.vsb.cz/duzi

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Content RussellRussell vs. Strawsonvs. Strawson: 100 years: 100 years’’ contensioncontension Topic-focus articulationTopic-focus articulation Outline of the proper division of labour between Outline of the proper division of labour between

Russellian and Strawsonian conceptions of definite Russellian and Strawsonian conceptions of definite descriptionsdescriptions

Foundations of TILFoundations of TIL The general analytic schema of sentences that come The general analytic schema of sentences that come

with a presupposition with a presupposition Conclusion: the moral to be drawn …Conclusion: the moral to be drawn …

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Proper names vs. definite descriptionsIndependently of any particular theory of proper names, it should be granted that

A proper proper name (as opposed to a definite description grammatically masquerading as a proper name) is a rigid designator of a numerically particular individual.

On the other hand, a definite description like, for instance, ‘the Mayor of Dunedin’, ‘the King of France’, etc., offers an empirical criterion that enables us to establish which individual, if any, satisfies the criterion at a particular state of affairs.

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Bertrand Russell (1905): On denotingThe contemporary discussion of the

distinction between names and descriptions was triggered by Russell (1905).

Russell’s key idea is the proposal that a sentence like

(1) The F is a G

is understood to have the logical form of (1′)

(1′) x (Fx y (Fy x=y) Gx)

rather than G(x Fx).

Russell in 1907

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‘On denoting’ – criticism the elimination of elimination of PeanoPeano’s descriptive operator’s descriptive operator ‘’

understood as ‘the only’, and deprived definite descriptions of deprived definite descriptions of their self-contained meaningtheir self-contained meaning.

Russell’s translation of simple sentences like “The F is a G” into the molecular form “There is an F and at most one thing is an F and this thing is a G” is rather enigmatic (disregarding structural similarity between analysandum and analysans)

the contention is about that Russell simply got the truth conditions wrong in important cases of using descriptions when there is no such thing as the unique Fno such thing as the unique F.

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Strawson, P. F. (1950): ‘On referring’ This criticism was launched by Strawson: Russell's theory predicts the wrong truth-conditions for sentences like

“The King of France is baldThe King of France is bald”.RussellRussell: currently FalseStrawsonStrawson: neither true nor false, neither true nor false, because

if false then “The King of France is The King of France is notnot bald bald” must be true, which in turn entails that there is the King of France, contra the assumption.

Russell in 1950:

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“The King of France is bald”StrawsonStrawson: If there is no present King of France, then an utterance

containing such an expression is somehow defective. Strawson held that sentences like these not only not only entailentail the

existence of the present King of France, but also presupposepresuppose his existence. If ‘the present King of France’ fails to refer, then the presupposition is false and the sentence fails to have a determinate truth value.

(Nevertheless, for Strawson, sentencessentences are meaningful in are meaningful in and of themselvesand of themselves, independently of the empirical facts like contingent non-existence of the King of France.)

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Russell (1957) in response … Suppose, for example, that in some country

there was a law that no person could hold public office if he considered it false that the the Ruler of the Universe is wiseRuler of the Universe is wise.

I think an avowed atheist who took advantage of Mr. Strawson’s doctrine to say that he did he did not hold this proposition falsenot hold this proposition false would be regarded as a somewhat shifty character. (Ludlow, 2007)

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And the contention goes on … Strawson himself in (1964) came to doubt whether the debate of

entailmententailment versus versus presuppositionpresupposition could be settled by “brisk little could be settled by “brisk little formal argument[s]”formal argument[s]”.

Donnellan (1966): there is a sense in which Strawson and Russell are both right (and both wrong)both right (and both wrong) about the proper analysis of definite descriptions, because definite descriptions can be used in (at least) two different ways.

On a so-called attributive use, a sentence of the form ‘The F is a G’ is used to express a proposition equivalent to ‘Whatever is uniquely F is G’. Alternatively, on a referential use, a sentence of the form ‘The F is a G’ is used to pick out a specific individual, a, and say of a that a is a G.

Donnellan suggested that Russell’s quantificational account of definite descriptions might capture attributive uses, but that it does not work for referential uses.

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And the contention goes on … LudlowLudlow in (2007): in some cases descriptions are Russellian

and in other cases they are Strawsonian. Kripke (1977, in response to Donnellan): the Russellian

account of definite descriptions could, by itself, account for both referential and attributive uses, and that the difference between the two cases could be entirely a matter of entirely a matter of pragmaticspragmatics, because there is an important distinction between what one literally says by an utterance and what one intends to communicate by that utterance.

Neale (1990) supported Russell’s viewRussell’s view On the other hand, a number of linguists have recently come

to Strawson’s defenseStrawson’s defense.

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And the contention goes on … FintelFintel, Kai von (2004). Would you believe it? Would you believe it? The The

King of France is Back!King of France is Back! (Presuppositions and Truth-Value Intuitions).

Here it might suffice to say that Strawson’s concerns have not delivered a knock-out blow to Russell’s theory of descriptions, and so this topic remains very much active.

Mind October 2005, vol. 114Mind October 2005, vol. 114: A Century Later (Stephen Neale, ed.)a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell's paper ‘On Denoting’

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My proposal: the proper division of labour

I am not goingI am not going to take into account Kripke’s Kripke’s pragmatic factorspragmatic factors like the intentions of a speaker, for this is irrelevant to a logical semantic irrelevant to a logical semantic theorytheory.

Instead, I am going to show that:

1)1) definite descriptionsdefinite descriptions are not deprived of their self-contained meaning and they denote one and the same entity in any context. Thus they are never Russellianare never Russellian.

2) Russell was nevertheless right in his insight that a definite definite description ‘the F’description ‘the F’ does not refer to a definite individual; rather, it denotes a conditiondenotes a condition to be contingently satisfied by the individual (if any) that happens to be the F.

I will explicate such conditions in terms of possible-world intensions, viz. as individual roles or offices to be occupied by at most one individual per world/time pair.

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My proposal: the proper division of labour

3) I am going to show that Donnellan was right that sentences of the form “The F is a G” are ambiguous.

4) their ambiguity does not concern a shift of does not concern a shift of meaningmeaning of the definite description ‘the F’. Rather, the ambiguity concerns different topic-focus articulations of these sentences (or different suppositions in which one and the same meaning occurs: de dicto vs. de re).

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My proposal: how to move beyond that dilemma; the proper division of labour Russell and StrawsonRussell and Strawson took themselves to be at loggerheads;

whereas, in fact, they spoke at cross purposesspoke at cross purposes. The received view still tends to be that there is room for at most

one of the two positions, since they are deemed incompatibledeemed incompatible. And they are, of course, incompatible – if they must explain the same set of data.

But they should notthey should not, in my view. One theory is excellent at explaining one set of data, but poor at explaining the data that the other theory is excellent at explaining; and vice versa.

My novel contributionnovel contribution advances the research into definite descriptions by pointing out how progress has been hampered by a false dilemma and how to move beyond that dilemmahow to move beyond that dilemma.

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topic-focus ambiguity a) Description ‘the F’ may occur in the topic of a

sentence and some G (the focus) is predicated about the topic: G(F).

This case corresponds to Donnellan’s referential use; using medieval terminology I will say that ‘the F’ occurs occurs with de re suppositionwith de re supposition. The sentence presupposes the existence of a unique F. Thus StrawsonStrawson’s analysis appears to be adequate for ‘topic’, i.e. de re cases.

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topic-focus ambiguity b) The other option is ‘G’ occurring in the topic and ‘the F’ in

the focus of the sentence: F(G).

This reading corresponds to Donnellan’s attributive use of ‘the F’ and the description occurs with de dicto suppositionde dicto supposition. On this reading the truth-conditions as specified by RussellianRussellian analysis. They do not presupposedo not presuppose, but only only entailentail, the existence of a unique F.

However, Russellian analysisRussellian analysis, though being equivalent to the one I am going to propose, is not an adequate literal analysisis not an adequate literal analysis of de dicto readings, because it deprives the semantically meaningful constituent ‘the F’ of its meaning.

c) NeutrNeutral readingal reading every definite description is connected with existential presupposition (Kai von FintelKai von Fintel)

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Murali Ramachandran (2009) tackled a similar problem (but did not analyse it)

Referring vs. Predicative use

“The tallest spy is John” – referring

“John is the tallest spy” – predicative

“John wants the murderer caught” – predicative

“The murderer is wanted by John to be caught” – referring

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Topic – Focus articulationTopic – Focus articulation Semantic or pragmatic problem? I am going to demonstrate the semantic nature of the

topic-focus difference by means of a logical analysis, using procedural semantics of Transparent Intensional Logic (TIL)

Moreover, the proposed solution of the definite the proposed solution of the definite description problem generalizes to any sentences description problem generalizes to any sentences differing in their topic-focus articulation.differing in their topic-focus articulation.

Topic presupposition Focus mere entailment

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Presupposition vs. mere entailment(i) P is a presupposition of S:

(S |= P) and (non-S |= P)Corollary: If non-P then neither S nor non-S is true; S has no truth-value.

(ii) S entails but does not presuppose P:(S |= P) and neither (non-S |= P) nor (non-S |= non-P)

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“AllAll students of Logicstudents of Logic enrolled in TU Ostrava enrolled in TU Ostrava winter term 2010 passed the final examwinter term 2010 passed the final exam”

Scenario 1: Q.: What about the students who signed up for the Logic course,

how did they do?A.: Oh well, they all passed the final exam. presuppositionpresupposition: There are some students enrolled in the Logic There are some students enrolled in the Logic

course in winter semestercourse in winter semester; if not (for instance, because the course runs in summer term), then no truth-value. For, the negated sentence cannot be true as well: “Some Some students who signed up for the Logic course did not pass the students who signed up for the Logic course did not pass the final examfinal exam”.

mere entailment: The final exam has taken place. Because, the sentence can be false for two reasons: Either some of the students did not succeed, or none of the

students succeeded because the exam has yet to take place.

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“AllAll students of Logicstudents of Logic enrolled in TU Ostrava winter enrolled in TU Ostrava winter term 2010 passed term 2010 passed the final examthe final exam”

Scenario 2:

Q.: What about the final exam in Logic, what are the results?

A.: Oh well, all students passed.

presuppositionpresupposition: The final exam The final exam have already taken placehave already taken place;

if it has not then no truth-value, because the negated sentence cannot be true as well: “The final examThe final exam has not been passed by all students” has not been passed by all students”

mere entailment: Some students signed up for the course …

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“AllAll students of Logicstudents of Logic enrolled in TU Ostrava winter enrolled in TU Ostrava winter term 2010 passed the final examterm 2010 passed the final exam”

First-order logic; FOL regimentation: (SL – students of logic …; SFT – success in final test):

x [SL(x) SFT(x)]But, every interpretation assigning an empty

set to SL is a model !No way to respect the truth-conditions

concerning presuppositions in FOLThe need for a richer framework TIL

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TIL in briefTIL in brief

Hyperintensional, typed, partial -calculus Infinite ramified hierarchy of types Basic notion: CConstruonstructionction

abstract, algorithmically structured procedureprocedure C

that consists of one or more particular steps, or constituents,constituents, that are to be individually executed in order to execute C.

procedureprocedure producing lower-order objects that can be Lower-order procedures, mappings, functional values

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TIL semantic schemaTIL semantic schema

Expression

expresses

Procedure (sense)

denotes produces

Denotation (if any)

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TIL Ontology (types of order 1)

Types of order 1 (non-structured objects) Basic (atomic) entities Basic (atomic) entities

truth-values {T, F} ()

universe of discourse {individuals} ()

times or real numbers ()

possible worlds () Functional (molecular) entitiesFunctional (molecular) entities::

( 1…n)

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Constructions

Variables x, y, p, w, t, … v-construct Trivialization 0C constructs C (of any type)

0Prime Prime/(), 0Student Student/()

Closure [x1…xn X] ( 1…n)

1 n

Composition [F X1 … Xn]

( 1…n) 1 n

Execution 1X, Double Execution 2X

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TIL Ontology (higher-order types)

Constructions of order 1Constructions of order 1 (1) construct entities belonging to a type of order 1o / belong to 1 : type of order type of order 22

Constructions of order 2 Constructions of order 2 (2) construct entities belonging to a type of order 2 or 1o / belong to 2 : type of order type of order 33

Constructions of order n Constructions of order n (n) construct entities belonging to a type of order n 1o / belong to n : type of order type of order n + 1n + 1

Functional (molecular) entitiesFunctional (molecular) entities:: ( 1…n) / belong to n

(n: the highest of the types to which , 1, …, n belong)

And so on, ad infinitum

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(i)(i) hyperintensional contextshyperintensional contexts constructionconstruction is not used to present an object, but is itself mentionedmentioned as functional argument

(though a hyperintension of one order higher needs to be used to mention this lower-order construction);

(ii)(ii) intensional contextintensional contextss construction is usedused to present a functionfunction without presenting a particular value of the function; moreover, the construction does not occur within another

hyperintensional context;

(iii)(iii) extensional contextextensional contextss construction is usedused to produce a particular valuevalue of the function at a given argument; moreover, the hyperintension does not occur within

another intensional or hyperintensional context.

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Construction Construction context-invariant meaning context-invariant meaning

Hyperintensional contextHyperintensional context construction (“function-in-intension”) is an object of predication (a

functional argument)“Tom is solving the equation sin x = 0”. existuje něco, co řeší

wt [0Solvewt 0Tom 0[[0SinSin x] = 00]]] wt c …

Intensional contextIntensional context function-in-extension is an object of predication

“Sine is a periodic function”[0Periodic 0SinSin] f [0Periodic ff]

Extensional contextExtensional context Functional value is an object of predication

“sin = 0”[[0SinSin 0] = 00] x [[0SinSin x] = 00]

Types: Periodic/(()); Sin/(); Solve/((1)); / ; Tom/; c n; f (); x .

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Partiality

TIL involves properly partial functions properly partial functions undefined for some or all of their arguments, and

improper constructionsimproper constructions, which fail to produce a product.

Improperness basically arises from the procedure of applying a properly partial function f to an argument a, such that f returns no value at a.

The procedure of functional application induces The procedure of functional application induces an extensional context. an extensional context.

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Improperness (non-existence)Improperness (non-existence)

stems from CompositionComposition used in an extensional contextextensional context: if F F has no-value at has no-value at aa (value gap) then

[0F 0a] is improper

and so is any C occurring extensionally and containing [0F 0a] as a constituent; partiality is strictly propagated partiality is strictly propagated upup::

[… [ … [0F 0a] …] …] is improper

until the context is raised up to hyper/intensionalhyper/intensional

intensionalintensional:: x… [… [ … [0F 0a] …] …] is properhyperintensionalhyperintensional:: 0[… [ … [0F 0a] …] …] is proper

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“AllAll students signed up for Logicstudents signed up for Logic passed the final exampassed the final exam”

The sense (scenario 1): If there are some students signed up for Logic

than T or F according as all of them passed the exam, else Fail (to produce a truth-value)

TIL analysis (schematic):

wwtt IfIf [ [00 [[00Students_signedStudents_signedwt wt 00LogicLogic] ]

than than [[[[00All All [[00Students_signedStudents_signedwt wt 00LogicLogic]]]]

00Passed_examPassed_examwtwt] ]

else Failelse Fail

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“AllAll students enrolled in Logicstudents enrolled in Logic passed the final exampassed the final exam”

Types. /(the existential quantifier (applied to a set

returns T if the set is non-empty, otherwise F); All/(restricted quantifier (applied to a set

M returns the set of all supersets of M);Students_for/(empirical function that

dependently on states of affairs (world andtime ) assigns to an individual a set of individuals (who are signed for);

Logic/; (for the sake of simplicity – individual)Passed_exam/property of individuals

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The King of France … StrawsonianStrawsonian reading:

“The King of FranceThe King of France is bald” RussellianRussellian reading:

“The King of France is baldbald”“Among the baldiesbaldies there is the King of France” you would most probably protest, “This cannot be true,

for there is no King of France now”. On such a reading the sentence is about baldnessthe sentence is about baldness

(topic)(topic), claiming that this property is instantiated by the King of France (focusfocus).

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The King of France … Strawsonian(S) wt [0Baldwt wt [0King_ofwt 0France]wt]

“The King of France is/is not bald”

“The King of France exists”Existential presupposition de rede re

“The King of France is bald”

“The King of France is Louis XVI”

“Louis XVI is bald” Substitution of co-referring terms (de rede re)

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The King of France … StrawsonianProofs:a) Existential presupposition1) [0Baldwt wt [0King_ofwt 0France]wt] assumption2) [0Improperwt 0[[wt [0King_ofwt 0France]]wt]] by definition of

Composition3) [0Empty x [x = [wt [0King_ofwt 0France]]wt]] obvious from (2)4) [0x [x = [wt [0King_ofwt 0France]]wt]] existential generalization5) [0Existwt [wt [0King_ofwt 0France]]] by def. of Exist.The proof from [0Watchwt wt [0King_ofwt 0France]wt] is analogous.

b) Substitution of v-congruent meanings (co-referring)1) [0Baldwt wt [0King_ofwt 0France]wt] assumption2) [0Louis = wt [0King_ofwt 0France]wt] assumption3) [0Baldwt 0Louis] substitution of identicals

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The King of France … Russellian

“The King of France is baldbald” True, if among the boldies there is the King of France False, if among those who are bald there is no King of

France (either because the present King of France does not exist or because the King of France is not bald).

(R)ussell: “There is a unique individual such that he is the King of France and he is bald.”

Russellian and Strawsonian analyses are co-entailing yet co-entailing yet not equivalentnot equivalent; they differ in those states-of-affairs where the office is vacant: (R) is False while (S) has no truth-value

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Russellian vs. Strawsonian

(R) |= (S) and (S) |= (R) but the two readings are not equivalent

Propositions are properly partial functions:<w1,t1> T<w2,t2> T<w3,t3> F<wi,ti> (Strawson) truth-value gap

(Russell) F<wj,tk> F<wl,tm> (Strawson) truth-value gap

(Russell) F

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The King of France … Russellian(R)ussell: “There is a unique individual such that he is the

King of France and he is bald.”

TIL (R1):

wt [0x [x = [wt [0King_ofwt 0France]wt] [0Baldwt x]]].

Does not deprive ‘the King of France’ of its meaning:

the context-invariant meaningcontext-invariant meaning wwtt [ [00King_ofKing_ofwtwt 00FranceFrance]]

Yet I am not content with TIL (R1).

Russell’s analysis has another defect: it does not comply with Carnap’s principle of subject matter (only those entities that receive mention in the sentence can become constituents of its meaning).

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Russell argued for his theory in (1905, p. 3):

“The evidence for the above theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur.

Of the possible theories which admit such constituents the simplest is that of Meinong. This theory regards any grammatically correct denoting phrase as standing for an object.

Thus ‘the present King of France’, ‘the round square’, etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects.

This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction.

It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round, etc.

But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred. “

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We have such a theory at hand

TILTIL, as a hyperintensionalhyperintensional, , typedtyped, , partialpartial -calculus, is in a much better position to solve the problem.

The difference consists in the way negated form is obtained.

StrawsonianStrawsonian: “The King of France is not bald” lacks a truth-value in those w, t-pairs where the office is vacant

RussellianRussellian: “It is not true that the King of France is bald” true in those w, t-pairs where the office is vacant

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Negation

StrawsonianStrawsonian: The property of not being bald in a <w,t> is ascribed to an individual (whoever, … if any)

RussellianRussellian: The property of not being true in a <w,t> is ascribed to the entire proposition Ptrue in those w, t-pairs were the office goes vacant.

[0Undefwt P] = [[0Truewt P] [0Falsewt P]]

[0Truewt P] = [[0Falsewt P] [0Undefwt P]]

[0Falsewt P] = [[0Truewt P] [0Undefwt P]]

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The King of France …Russellian(R*)wwtt [ [00TrueTruewtwt wwt t [[00BaldBaldwtwt wwtt [ [00King_ofKing_ofwtwt 00FranceFrance]]wtwt]]]]

neither (R*) nor its negation

(R*_neg)wwtt [[00TrueTruewtwt wwtt [ [00BaldBaldwtwt wwtt [ [00King_ofKing_ofwtwt 00FranceFrance]]wtwt]]]]

entails that the King of France exists, which is just as it should be.

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Some more examples (topic-focus)“The King of FranceThe King of France visited London yesterday”Presupposes that the King of France exists now (at t)

wt [x t’[[[0Yesterday t] t’] [0Visitwt’ x 0London]] wt [0King_ofwt 0France]wt]

“LondonLondon was visited by the King of France yesterday”Merely entails that the King of France existed yesterday (at

some t’ belonging to yesterday)

wt t’[[[0Yesterday t] t’] [0Visitwt’ wt [0King_ofwt 0France]wt’ 0London]]

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Some more examples (topic-focus)(A) “The globalglobal financial andfinancial and economic crisiseconomic crisis was caused by

the Bank of America”Presupposes that there be a global financial and economic crisisMerely entails that the Bank of America exists

wt [if 0Crisiswt then [0Truewt wt [0Causewt 0Bank_of_Americawt 0Crisis]] else Fail]

(B) “The Bank of AmericaBank of America caused the global financial and economic crisis”

Presupposes that the Bank of America existsMerely entails that there is a global financial and economic crisis

wt [if [0Existwt 0Bank_of_America] then [0Truewt wt [0Causewt 0Bank_of_Americawt 0Crisis]] else Fail]

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If P then C else D[[P C] [P D]]

is not an adequate analysis, because both C and D

are executed; if one of them fails, the whole Composition fails.

If-then-else: a non-strict function, not complying with the principle of Compositionality?

No cogent reason for non-strictness! We need a ‘lazy evaluation’.

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If P then C else D: a two-phase instruction

1. Make a choice between C and D based on P: [0The_only c [[P [c = 0C]] [P [c = 0D]]]]

2. Execute the chosen construction c

2[0The_only c [[P [c = 0C]] [P [c = 0D]]]] The_only is a singulariser function ({n} n) that returns the

only construction, the member of a singleton; otherwise undefined

c n: a variable ranging over procedures; 0C, 0D: procedures C, D are objects to operate on; Hyperintensional logic is needed to deal with procedures,

not only with their products.

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General analytic schema

If If PresuppositionPresupposition P P then then C C else else FailFail (to produce a truth-value)

2[0The_only c [P [c = 0C]]]

TIL-Script (computational variant of TIL)TIL-Script (computational variant of TIL); ; functional programming language

The inference machine is based on the generalized -rule ‘by value’ applicable to -rule ‘by value’ applicable to properly partial functionsproperly partial functions

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Concluding remarks Logical analysis cannot disambiguate any sentence,

because it presupposes full linguistic competence. Yet, our fine-grained method can contribute to a

language disambiguation by making these hidden features explicit and logically tractable.

In case there are more senses of a sentence we furnish the sentence with different TIL constructions.

Having a formal fine-grained encoding of a sense, we can then automatically infer the relevant consequences.

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The moral to be drawn … The Babel tower God multiplied languages But even within one language we often do not

understand each other due to ambiguities a lot of misunderstanding, confusion, … Holy Spirit gave us wisdom, tolerance, the ability to

listen to each other … in Bible there are many such ambiguities and we

cannot read it literally, we should read it carefully, taking into account historical situation

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References: http://www.cs.vsb.cz/duzi/

Duží, M., Jespersen, B., Materna, P.: Procedural Semantics for Procedural Semantics for Hyperintensional LogicHyperintensional Logic; ; Foundations and Applications of Foundations and Applications of Transparent Intensional Logic.Transparent Intensional Logic. Springer 2010.

Duží, M. (2008): ‘TIL as the Logic of Communication in a Multi-‘TIL as the Logic of Communication in a Multi-Agent System’Agent System’. In Research in Computing Science, vol. 33, pp. 27-40.

Duží, M. (2009): ‘‘Topic-Focus Articulation from the Semantic Point Topic-Focus Articulation from the Semantic Point of Viewof View’’, in CICLing 2009. Ed. Gelbukh Alexander, Berlin Heidelberg: Springer-Verlag LNCS, vol. 5449, pp. 220-232.

Tichý, P. (2004): : Collected Papers in Logic and PhilosophyCollected Papers in Logic and Philosophy, V. Svoboda, B. Jespersen, C.Cheyne (eds.), Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press.

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If questions then answers else Fail

Thank you for your attentionThank you for your attention