The elimination of metaphysics

The attitude of Logical Positivism towards metaphysics is well expressed by Carnap in the article 'Überwindung der Metaphysik durch Logische Analyse der Sprache' in Erkenntnis, vol. 2, 1932 (English translation 'The Elimination of Metaphysics Through Logical Analysis of Language' in Sarkar, Sahotra, ed., Logical empiricism at its peak: Schlick, Carnap, and Neurath, New York : Garland Pub., 1996, pp. 10-31). A language – says Carnap – consists of a vocabulary, i.e. a set of meaningful words, and a syntax, i.e. a set of rules governing the formation of sentences from the words of the vocabulary. Pseudo-statements, i.e. sequences of words that at first sight resemble statements but in reality have no meaning, are formed in two ways: either meaningless words occur in them, or they are formed in an invalid syntactical way. According to Carnap, pseudo-statements of both kinds occur in metaphysics.

A word W has a meaning if two conditions are satisfied. First, the mode of the occurrence of W in its elementary sentence form (i.e. the simplest sentence form in which W is capable of occurring) must be fixed. Secondly, if W occurs in an elementary sentence S, it is necessary to give an answer to the following questions (that are – according to Carnap – equivalent formulation of the same question):

• (1.) What sentences is S deducible from, and what sentences are deducible from S?
• (2.) Under what conditions is S supposed to be true, and under what conditions false?
• (3.) How S is to verified?
• (4.) What is the meaning of S?

(Carnap, 'The Elimination of Metaphysics Through Logical Analysis of Language' in Sarkar, Sahotra, cit., pp. 12)

An example offered by Carnap concerns the word 'arthropod'. The sentence form "the thing x is an arthropod" is an elementary sentence form that is derivable from "x is an animal", "x has a segmented body" and "x has jointed legs". Conversely, these sentences are derivable from "the thing x is an arthropod". Thus the meaning of the words 'arthropod' is determined.

According to Carnap, many words of metaphysics do not fulfil these requirements and thus they are meaningless. As an example, Carnap considers the word 'principle'. This word has a definite meaning, if the sentence "x is the principle of y" is supposed to be equivalent to the sentence "y exists by virtue of x" or "y arises out of x". The latter sentence is perfectly clear: y arises out of x when x is invariably followed by y, and the invariable association between x and y is empirically verifiable. But – says Carnap – metaphysicians are not satisfied with this interpretation of the meaning of 'principle'. They assert that no empirical relation between x and y can completely explain the meaning of "x is the principle of y", because there is something that cannot be grasped by means of the experience, something for which no empirical criterion can be specified. It is the lacking of any empirical criterion – says Carnap - that deprives of meaning the word 'principle' when it occurs in metaphysics. Therefore, metaphysical pseudo-statements such as "water is the principle of the world" or "the spirit is the principle of the world" are void of meaning because a meaningless word occurs in them.

However, there are pseudo-statements in which occur only meaningful words; these pseudo-statements are formed in a counter-syntactical way. An example is the word sequence "Caesar is a prime number"; every word has a definite meaning, but the sequence has no meaning. The problem is that "prime number" is a predicate of numbers, not a predicate of human beings. In the example the nonsense is evident; however, in natural language the rules of grammar do not prohibited the formation of analogous meaningless word sequences that are not so easily detectable. In the grammar of natural languages, every sequence of the kind "x is y", where x is a noun and y is a predicate, is acceptable. In fact, in the grammar there is no distinction between predicate which can be affirmed of human beings and predicate which can be affirmed of numbers. So "Caesar is a general" and "Caesar is a prime number" are both well-formed, in contrast for example with "Caesar is and", which is ill-formed. In a logically constructed language – says Carnap – a distinction between the various kinds of predicate is specified, and pseudo-statements as "Caesar is a prime number" are ill-formed. Now, and this is the main point of Carnap's argument, metaphysical statements in which do not occur meaningless words, are indeed meaningless because they are formed in a way which is admissible in natural languages, but not in logically constructed languages. Carnap attempts to indicate the most frequent sources of errors from which metaphysical pseudo-statements can arise. One source of mistakes is the ambiguity of the verb 'to be', which is sometimes used as a copula ("I am hungry") and sometimes to designate existence ("I am"). The latter statement incorrectly suggests a predicative form, and thus it suggests that existence is a predicate. Only modern logic, with the introduction of an explicit sign to designate existence (the sign $\exists \;$), which occurs only in statements such as $\exists \;xP(x)$, never as a predicate, has showed that existence is not a predicate, and thus has revealed the logical error from which pseudo-statements such as "cogito, ergo sum" has aroused.

Another source of mistakes is type confusions, in which a predicate of a kind is used as a predicate of another kind. For example the pseudo-statements "we know the Nothing" is analogous to "we know the rain", but while the latter is well-formed, the former is ill-formed, at least in a logically constructed language, because 'Nothing' is incorrectly used as a noun. In a formal language, 'Nothing' only means $\lnot \;\exists \;x$, such as "there is nothing which is outside", i.e. $\lnot \;\exists \;xO(x)$, and thus 'Nothing' never occurs as a noun or as a predicate.

What is the role of metaphysics? According to Carnap, although metaphysics has not theoretical content, it has content indeed: metaphysical pseudo-statements express the attitude of a person towards life. Metaphysics is an art like lyrical poetry. The metaphysician, instead of using the medium of art, works with the medium of the theoretical; he confuses art with science, attitude towards life with knowledge, and thus produces an unsatisfactory and inadequate work. "Metaphysicians are musicians without musical ability" (Carnap, 'The Elimination of Metaphysics', in Sarkar, Sahotra, cit.,p. 30).

Although the anti-metaphysical stand is firm in Carnap's philosophy, the ground of rejecting metaphysic slightly changed, and the analysis and description of metaphysics changed also.

In the late 30's Carnap emphasyzed the distinction of formal and material mode of speech. Metaphisics was characterized in this era by Carnap as sentences, formulated in material mode of speech, which usually can be corrected by putting them in formal mode of speech.

Later, in Empiricism, Semantics and Ontollogy Carnap developed a theory of frameworks. He distingishued external and internal questions relative to the framwework. According to Carnap internal theoretical questions can be answered. Fopr example in arithmetic, one can decide and prove that "there exists no even prime number larger than 2". On the other hand the question "Are numbers really existing?" is not an internal question. This question as an external theoreticasl question is meaningles and usually these are the methaphysical questions.

External questions however can be put as practical questions "is the system of arythmetic useful in science? I.e. shall we accept the system as a tool?"