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Formalism and natural language in analytic philosophy

Tradition, doctrine and method

The definition of analytic philosophy remains ambiguous to the point that it has been argued that it is “preferable to speak of analytic philosophies in the plural.” It can be clarified by distinguishing three uses of expression: tradition, doctrine and method.

As a tradition, analytical philosophy begins with Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein in the early twentieth century. The original questions can be explained by the following questions:

  • Can we philosophize by following a scientific method?
  • Can we introduce more rigor in philosophy by proceeding by logic?
  • Can philosophy be reduced to logic?

The doctrines most often mentioned are logical positivism and logical atomism; but the expression may also refer to the philosophy of ordinary language, the philosophy of common sense, or a mixture of several doctrines. This practice was common until the 1950s, when analytical philosophers were generally engaged in a research program related to these doctrines.

The method of analytic philosophy is a general approach to philosophy which, through the analysis of language, rests on a strong technical and philosophical development of logic. Following an ancient tradition of Anglo-Saxon empiricism, which is already to be found in Locke, it sought, through logic, to clarify the meaning of utterances and thereby dispel “false problems”. This method is nowadays conceived not as a program but as a concern for clarity and precision, requiring an important place for argumentation using the processes of formal logic.

Formalism and natural language

The purpose of the analytical approach is to clarify the philosophical problems by examining and clarifying the language used to formulate them. This method counts, among its major contributions, modern logic, the uncovering of the problem of meaning and denotation in the construction of meaning, Kurt Gödel’s incompleteness theorem, Russell’s theory of defined descriptions, the refutability of Karl Popper, Alfred Tarski’s semantic theory of truth.

The two main branches of analytic tradition are, on the one hand, the search for understanding language by using formal logic, i.e. to formalize and solve philosophical questions on the basis of this formulation; on the other hand, research to understand philosophical ideas by examining in particular the natural language used to formulate them and to clarify them on the basis of this examination. These two types of research are sometimes completely opposed, but sometimes identical. Wittgenstein began with the first type of research, and then continued his research in the natural language.


Logical atomism and ideal language

For authors like Gottlob Frege, Bertrand Russell, Rudolf Carnap or even Willard Van Orman Quine, natural language is confused, simplistic, full of errors and must be reformulated in a formal, rigorous and unambiguous language, (See, for example, Frege’s article: That science justifies a recourse to ideography). This formalization does not only have consequences on how to express a problem: it raises the question whether some of the old problems should not be eliminated at the same time. For example, if the problems posed by popular psychology are meaningless, should we conclude that our usual conceptions of the mind are fictions?

The origin of analytic philosophy is to be found in Frege’s development of the calculation of predicates which has allowed logical formalization to be extended to a greater number of utterances. Similarly, Russell and Whitehead set themselves the goal, in their Principia Mathematica:

  • to show that mathematics and logic can be reduced to mathematical logic;
  • to show that the logical result is an ideal language.

Russell considered logical formalism as an indispensable tool for exposing the fundamental structures of philosophical problems. For example, he consider that the copula “is” can be analyzed in three distinct ways:

  • “the cat is asleep”: the is of predicate means that x has the property P, that is P(x)
  • “she is a cat”, or “there is a cat”: the is of existence means that there is an x, that is: ∃(x)
  • “three is half of six”: the is of identity means that x is identical to y, that is x = y

Russell thus attempted to solve various philosophical problems by applying such clear and precise distinctions, the best known example being the statement “actual King of France,” which for Frege did not make sense because it lacked a real referent. This attempt is based on the foundational thesis of logical atomism that the structure of reality is essentially the same as mathematical logic. Hence, all problems have a logical formulation.

The Tractatus

Ludwig Wittgenstein is considered to have developed Russell’s logical atomism in a brief and difficult book, the Tractatus logico-philosophicus: this book is considered to be one of the most important philosophical books of the twentieth century. The general objective is to trace, from the interior of the language, limits beyond which propositions are meaningless. Wittgenstein’s remarks (especially on his work itself) cast doubt, ultimately, on the ultimate possibility of logic. The construction and complexity of the Tractatus are such that the text will be misunderstood by the members of the Vienna circle, resulting in a definitive separation between them and the author, following a meeting.

Wittgenstein states that the world is the existence of facts; these states of fact can be expressed in a logic of the first-order predicates. As a result, a picture of the world can be realized by expressing atomic facts in atomic propositions and linking them by logical operators.

“5.6 The boundaries of my language are the boundaries of my world.”

This thesis is one of the reasons for the close relationship between philosophy of language and analytic philosophy: from this point of view, language is the principal, or the only, tool of philosophy. Thus, for Wittgenstein, and for many other analytical philosophers, philosophy aims to clarify the use of language. By this method, the hope is to see resolved all philosophical problems when the language will be used with perfect clarity. Wittgenstein considered, moreover, to have stated the definitive solutions of all philosophical problems:

“Nevertheless, the truth of the thoughts communicated here seems intangible and definitive. My opinion is that I have essentially resolved the problems in a decisive way.”

However, this last quote can be misunderstood by a reader who is too pressed. A clue, the disagreement with the circle of Vienna, nevertheless suggests its distance from its own work.

He left and became a teacher. But he came back later on to affirm the inadequacy of logical atomism, and he brought new developments in his posthumous work, the Philosophical Investigations (1953), considered as one of the founding works of the philosophy of ordinary language, which develops in radical opposition to the logical formalism of Frege, Russell and the first Wittgenstein himself.

Natural language

The philosophy of ordinary language (sometimes also called linguistic philosophy) is a current of analytical philosophy, represented by the second Wittgenstein, John L. Austin, John Searle, Paul Grice, etc.), which seeks to avoid excess formalism Attention to the usages and practices of ordinary language and common sense. According to this theory, meaning depends not only on the formal semantics of utterances, but also on pragmatics, that is, on the conversational context. The return to ordinary language is a reaction against the origins of analytic philosophy, which has sometimes been called the “philosophy of ideal language.”

Critics of analytic philosophy

The defenders of analytic philosophy argue that it has an objective of clarity and precision in the description of philosophical problems, which brings philosophy closer to the methodology of scientific disciplines. This clarity in the description of problems and the formulation of solutions makes it possible to avoid the ambiguity and difficulties of interpretation often blamed on “literary” philosophy. Analytical philosophy is also characterized by a concrete approach, “by problems”. This way results a precise description of clearly identified philosophical problems for which a solution should be sought. Among these problems are: the paradox of the liar, the paradox of Hempel, etc.

(Analytical philosophy would see existence only from a logical point of view, like the Newton drawn by Blake: absorbed by figures, symbols of the scientific knowledge of nature, he does not contemplate it directly.)

Critics of analytic philosophy believe that this is merely a normative injunction to clarity and rigor, and that this describes more a tradition, periodicals, common readings and references, recurring examples and problems, than a true scientific “method”. Moreover, logical reduction is judged too superficial, whereas continental philosophy considers going back to the very conditions of metaphysics, ie, according to Heidegger, to an opening to being which would precede any logico-metaphysical categorization and which would therefore be more fundamental, deeper.

Although vivid criticisms were made against metaphysics by the first analytical philosophers (see, for example, The Exceedance of Metaphysics by Logical Analysis of Language by Carnap), these have since been largely tempered, the positivist program of the Vienna Circle was generally considered a failure, although instructive. Today, analytical and metaphysical philosophy are not contradictory (see Peter Strawson or Frederic Nef).

Translated from Wikipedia

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