LOGIC In general usage, the process of reasoning and sound judgement, often taken to be the outcome of adequate education, an aspect of common sense, or both:
a logical decision. In philosophy, the study and development of close reasoning, especially inference, traditionally the concern of logicians and mathematicians and currently important for computer programmers, computational linguists, and researchers into artificial intelligence. There are several kinds of logic, such as
formal logic and
symbolic logic, of philosophical systems that acknowledge its influence, such as
logical positivism, and of techniques considered to incorporate logic, such as
logic arrays and
logic circuits in electronic technology.
Classical logic
The term
logikḗ was coined by the Greek philosopher Alexander of Aphrodisias in the 3c, but systems of organized thinking had already developed well before this in Greece, India, and China. Western culture has inherited the Greek tradition mainly through Rome and the Arab world. In this tradition, logic is closely linked with grammar and rhetoric, and discussion of one often leads to discussion of the others. For the Greeks, both reasoning and language were encompassed in the word
lógos, which they contrasted with
mûthos, a term that encompassed words, speech, stories, poems, fictions, and fables. Plato (5c BC) in
The Republic represented Socrates as wishing to exclude poetry from the proper education of the young, and after some 2,500 years, this viewpoint still carries weight: logic, science, and reason are commonly set on one side and poetry, art, and myth on the other. To make his case, however, Plato used many devices from poetry and rhetoric: he so structured his dialogues that Socrates always won, often with the help of poetic analogies such as the Simile of the Cave. His pupil Aristotle laid the foundations of logic proper, as the study of inference from
propositions arranged as formal
arguments.
Grammar and logic
Because logic and GRAMMAR developed together they have overlapping terminologies: both use the term
sentence, and deductive logic consists of a
logic of propositions (also called
sentential logic) and a
logic of predicates (also called a
logic of noun expressions). Logicians, grammarians, and rhetoricians are all interested in such matters as
AMBIGUITY,
FALLACY, paradox, syntax, and
SEMANTICS, and in such modalities as necessity, possibility, and contingency; linguists who are concerned with grammar, computation, and artificial intelligence take as much interest in logic as in natural language. Logicians and mathematicians have created systems that contain both sets of abstract symbols and the rules necessary for their combination and manipulation in strings. Such symbols, rules, and strings are often idealizations of elements in, or thought to be in, natural language (but isolated from such everyday factors as dialect variation, personal idiosyncrasy, figurative usage, emotional connotation, colloquial idiom, social attitude, and semantic change). When such a system of symbols is adapted to practical ends, however, as in computer technology and artificial intelligence,
pure logic becomes
applied logic, operating within a real machine intended to do real work in real time.
Although many logicians, grammarians, and linguists have been interested in a universal calculus of language (something that would transcend natural language or allow the dispassionate description of all language), they have built their systems out of the natural languages that they know best: Greek for Aristotle and his disciples, Latin for medieval and Renaissance grammarians, and English for such present-day theorists as Noam Chomsky. Both prescriptive and descriptive grammarians of such Western languages as French and English have been influenced by logic and by the languages in which the principles of logic developed. Because it emerged in large part through the use and analysis of language, it has not been difficult to find quasi-logical patterns in language. Some analysts have been inclined to see logical orderliness either as inherent in language or as a reasonable goal of language planning, especially when a language is in the process of being standardized. Everyday language, however, has a persistent (even frustrating) tendency towards the illogical or non-logical, as for example in the use of double negatives (
I didn't do nothing, which does not therefore mean ‘I did something’) and in idiomatic expressions (such as
it's raining cats and dogs).
All analysts of language work towards orderliness, but some go further and engage in or recommend making certain aspects of language, such as the spelling of English, more ‘regular’ (that is, more rule-governed and therefore more logically consistent). They may also favour an artificial language such as Esperanto or Basic English that is (apparently) free from the illogic of natural language. Interest in such reforms has often gone hand in hand with particular conceptions of and assumptions about, progress, science, efficiency, education, literacy, and standards. Logic has therefore been used as a tool for both the description of natural language and its prescriptive improvement. In the development of the first grammars of English, the model was Latin and the analytical terms were Greek as used by the describers of Latin. Medieval and Renaissance models for vernacular prose as a vehicle of rational discourse were either Latin prose or vernacular prose written in the Latin style. Theories of sentences and parts of speech were those developed by classical grammarians and logicians, often the same people. The analysis of sentences into subjects and predicates, main and subordinate clauses, and the like, has paralleled the logician's view of propositions as the core of language and of binary division as a powerful conceptual tool.
The limits of logic
In the second half of the 20c, ancient practice has gained fresh impetus through the work of Noam Chomsky. Some features of his work are: (1) The definition of a language as a set of well-formed sentences, indefinite in number. (2) Abstract and diagrammatic analyses of sentences of standard written English. (3) The use of quasi-logical symbols such as S for sentence, NP for noun phrase, and VP for verb phrase, to sustain the analysis of such sentences. (4) Logical transformations performed on strings of symbols so as to produce further strings. (5) The creation of a generative grammar, that is, a set of explicit, formal rules that specify or generate all and only the sentences which constitute a language; in so doing, they are seen as demonstrating the nature of the implicit knowledge of that language possessed by an ideal native speaker-hearer. Such an approach has often been taken to be a break with the past, but is rooted in more than two millennia of logical and grammatical system-building. It remains a matter of debate whether natural language can be handled by linguistic theories that derive in the main from or are closely associated with aspects of formal logic. Natural language is a neural mechanism, apparently the result of genetic and social evolution. While it is sometimes regular, logical, and precise, it is as often irregular, non-logical, and imprecise, and oftener still a mix of the two. It blends intellect with instinct, logic with inspiration, and the standard with the varied. Logic is closely associated with language and with its description and discussion in literate societies. As such, it is an essential tool, but one cannot deduce from this usefulness that it is the sole or even primary means by which natural language can be understood.
