Logic as representation and perfection of meaning

Our exposition of the propositional connectives and, or, not and if . . . then has revealed that their truth-functional definitions are quite often counter intuitive and unnatural, failing to correspond to the norms of ordinary English. None of the operators corresponds perfectly with any English equivalent (see Bach 2002 for further discussion). The discontinuity between natural language and and & has already been discussed in Chapter 4 (see 4.3.1); another example of the discontinuity between natural language and logical operators is provided by negation: given principles which we have not made fully explicit here but which are reasonably obvious, two negatives cancel each other out, giving a positive statement. Thus, the proposition ¬ ¬p is logically equivalent to p. This logical principle is well understood by educated speakers of English, who regularly avoid the use of double negatives like those in (24):

Constructions like this were once common in English; their decline only started in the seventeenth century (Martínez 2003: 478). The prescriptive grammatical tradition of English has proscribed the use of such double negatives for hundreds of years; nevertheless, the double negative continues to thrive ‘as a regular and widespread feature of non-standard dialects of English across the world’ (Huddleston and Pullum 2002: 847). Furthermore, in many languages, such as Spanish (25a), Italian (25b), Portuguese (25c) and Ancient Greek (25d), double negatives regularly per form a reinforcing, rather than a cancelling function:

Another particularly flagrant example of discontinuity between the operators and natural language is provided by the material conditional; indeed, the correspondence between) and ordinary language has been a matter of philosophical controversy since the time of Stoic logicians in antiquity. Case (d) of the truth table is the most problematic, since it means that a statement is automatically true where the antecedent is false and the consequent is true. But this seems to fly in the face of our intuitions about ordinary language. To borrow Girle’s example (2002: 240), why should it be automatically true that If Henry VIII was a bachelor then he was King of England? As Girle comments (2002: 240), many people ‘would want to say that it’s very difficult to say whether it’s true or false. To say it’s automatically true is too much.’ The truth-functional definition of) therefore seems not at all accurate as a representation of the meaning of English if . . . then. This is not a peculiarity of English: conditional expressions in other languages seem to be like English, and unlike), in this respect.

 We will see more examples of discrepancies between logic and ordinary language later in the chapter, and logicians have expended considerable effort to reconcile the two. The theory of conversational implicature developed by Grice, discussed in 4.3, is one such attempt. This theory leaves the truth-functional definitions of the operators intact, but there have been other attempts to amend the truth tables in order to bring the meanings of the operators into line with their natural language equivalents. For rea sons that go beyond the scope of this chapter, however, no one satisfactory way of doing this has ever gained wide acceptance: it would seem that we are stuck with the operators in their current state.

The clash between the meanings of the logical operators and their ordinary language equivalents reveals a contrast between two different interpretations of the nature of logic: logic as a representation and logic as a perfection of meaning. The two construals carry very different implications for the relevance of logic to linguistic semantics. According to the first view of logic, the truth-functional definitions of logical operators like ¬, &, and ) represent fundamental categories of human thought, and, as such, underlie the meanings of natural language at a certain degree of abstraction. Even though actual natural languages typically do not contain words whose meanings correspond to those of the logical operators, this does not mean that the logical operators are not representative of the meanings relevant to the analysis of natural language, nor that logic as a whole has nothing to do with the study of natural language. For McCawley (1981), for example, there is no clash between logic and linguistics: the two disciplines share a subject matter: meaning. Many linguists, indeed, would maintain that discontinuities between natural language and logic like those discussed in this section are to be explained by the fact that natural languages possess a pragmatic dimension which prevents the logical operators from finding exact equivalents in ordinary discourse. The fact that logical notions like ¬, &, and) are not transparently reflected in natural language is in itself no reason to doubt their importance as fundamental primitives of meaning, any more than the fact that people cannot draw freehand circles means that we do not have a concept CIRCLE. ‘Formal’ semantic theories in linguistics assume precisely that the principles of logic form part of a viable model of natural language meaning.

According to the second view of the relation of logic to natural language, logic does not distil principles already present in natural language, but transcends and perfects natural language. While logical principles may reveal the fundamental workings of thought, their utility lies precisely in that they allow us to escape the inadequacies of ordinary language. For Grice (1989), the fact that discrepancies exist between logical operators and their natural language equivalents ‘is to be regarded as an imperfection of natural languages’: the natural language expressions corresponding (imperfectly) to the logical operators ‘cannot be regarded as finally acceptable, and may turn out to be, finally, not fully intelligible’ (1989: 23). Natural language is not, therefore, to be appealed to in logical investigation, and the validity of logic has nothing to do with whether it turns out to be useful as a representation of natural language meaning.

This second view is appealing to logicians who see the principal purpose of logic as being to provide a solid basis for accurate reasoning of the sort required by science. Wittgenstein sums up this point of view when he says that ‘the crystalline purity of logic was of course not a result of investigation; it was a requirement’ (1953: §107): in other words, the value of logic is precisely that it takes us beyond the imperfections of natural language, allowing us to discern logical structures which the messiness of natural language obscures. As Barwise and Perry comment (1983: 28), the principal concern of the founders of modern logic – Frege, Russell and Whitehead, Gödel, and Tarski – was to provide a sure footing for the study of mathematics, and hence of science. This meant that logical investigation was in fact often oriented away from natural language, embodying assumptions designed to put mathematical notions on a sound footing, which have made it ‘increasingly difficult to adapt the ideas of standard model theory to the semantics of natural languages’.

اخر الاخبار

اخبار العتبة العباسية المقدسة

قسم رعاية الصحن الشريف ينشر لافتات الحزن بذكرى شهادة الإمام الجواد (عليه السلام)

قسم العلاقات العامة يقيم مجلس عزائه الأسبوعي لاستذكار فضائل أهل البيت (عليهم السلام)

متحف الكفيل يستعرض درعًا هنديًّا يعود إلى القرن التاسع عشر

ضمن محفلها الأسبوعيّ.. دار علوم نهج البلاغة تقدّم محاضرةً عن تحرير الإنسان من قيود المنصب

المزيد

الآخبار الصحية

طريقة مبتكرة للكشف المبكر عن أمراض القلب والشرايين

منظمة الصحة تحذر من خطر إدمان الشباب لأكياس النيكوتين

خبراء يحذرون من عادة شائعة تهدد صحة الملايين

خبير يكشف 5 حقائق طبية صادمة وغير معروفة

المزيد

الآخبار التكنلوجية

الأولى في العالم.. الصين تجري تجربة رائدة في الفضاء باستخدام "جنين اصطناعي"

دراسة حديثة تفند ربط التستوستيرون بالمخاطرة لدى الرجال

ميتا تضيف وضع "المحادثة المخفية" إلى تطبيق "واتساب"

فوبيا المرتفعات ليست من الدماغ.. دراسة تكشف السبب

المزيد

مواضيع ذات صلة

Propositional logic

Validity, soundness and logical form

Polysemy and monosemy as a cline

Tests for polysemy

Polysemy, monosemy and homonymy

Polysemy and meaning division

Componential analysis

Connective Adjuncts

Synonymy

Taxonomy

Hyponymy

Meronymy