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Notes by RBJ on

Philosophy and Logical Syntax

by Rudolf Carnap

Lecture IThe Rejection of Metaphysics
Section 1Verifiability
Section 2Metaphysics
Section 3Problems of Reality
Section 4Ethics
Section 5Metaphysics as Expression
Section 6Psychology
Section 7Logical Analysis
Lecture IILogical Syntax of Language
Section 1"Formal" Theory
Section 2Formation Rules
Section 3Transformation Rules
Section 4Syntactical Terms
Section 5L-terms
Section 6Content
Section 7Pseudo-Object Sentences
Section 8The Material and the Formal Modes of Speech
Lecture IIISyntax as the Method of Philosophy
Section 1The Material Mode of Speech
Section 2Modalities
Section 3Relativity in Regard to Language
Section 4Pseudo-questions
Section 5Epistemology
Section 6Natural Philosophy
Section 7What Physicalism Asserts
Section 8What Physicalism Does not Assert
Section 9The Unity of Science


These lectures are concerned with explaining the method of philosophising being practiced by the Vienna Circle in 1934. This is the method of the syntactical analysis of scientific language.

Lecture 1 - The Rejection of Metaphysics

Section 1 - Verifiability

Philosophy is considered as having three components, Metaphysics, Psychology and Logic, the present work falling into the latter category and being characterised as Logical Analysis.

The purpose of Logical Analysis is to analyse assertions and make clear their sense, which involves determining their method of verification. Some propositions can be directly verified, others are to be verified indirectly, by directly verifying propositions deduced from them. Indirectly verifiable propositions cannot be conclusively verified. Propositions which have no verifiable consequences are without sense, "nothing but an empty series of words".

Section 2 - Metaphysics

Propositions purporting to be metaphysical either are un-verifiable, and hence have no sense, or else they are properly a part of empirical science, not of metaphysics.

Section 3 - Problems of Reality

Philosophical (as opposed to physical) questions about reality, sometimes considered to be a part of epistemology, are in fact metaphysics, and hence lack sense. This includes doctrines such as realism, idealism, and even positivism. But not logical positivism, which is a logical thesis.

Section 4 - Ethics

Philosophical or normative ethics, in which statements expressing general ethical principals are asserted, should be distinguished from sociological or psychological studies related to ethics, which are a part of science. Statements expressing ethical principles are in fact overt or covert imperatives, even when they are expressed as value judgements which appear to be assertions rather than commands. Considered as assertions they lack sense and "therefore we assign them to the realm of metaphysics".

Section 5 - Metaphysics as Expression

Metaphysical statements, though they lack sense, do not fail to express something. They express something in a manner similar to the way in which artistic communications such as poems and music may express feelings. However, metaphysical statement deceptively appear to have a representative function (i.e. they appear to assert something) as well as an expressive one, and for this reason they should be rejected.

Section 6 - Psychology

Psychology should be clearly distinguished from logic and is a part of empirical science, not philosophy.

(= The System of Theoretical Knowledge)
Lyrical Verses, etc.
Empirical Sciences
Physics, Biology, etc.

Section 7 - Logical Analysis

"The only proper task of Philosophy is Logical Analysis." Logical analysis consists in determining the character of various propositions or pseudo-propositions (which as far as I can tell from this section seems to mean determining whether they are logical, scientific, or senseless).

Wittgenstein's view that the Tractatus is meaningless is rejected, and this lecture is affirmed to be an example of logical analysis. It is the purpose of the following lectures to give reasons for this claim, to show a way of formulating the results of logical analysis, and thus to exhibit an exact method of philosophy. (from which we may infer that logical analysis goes beyond characterising a proposition as logical or scientific, by providing a formal translation of the proposition.)

Lecture II - The Logical Syntax of Language

Section 1 - "Formal" Theory

The Logical Syntax of a language is the formal theory of that language. "Formal" means, exclusively concerned with syntax, "without any reference to sense or meaning". This is an extension of Hilbert's metamathematics to "the whole language-system of science".

Section 2 - Formation Rules

A language consists of a system of rules, which may be either formation rules or transformation rules. Formation rules determine how sentences of the language can be constructed. They are like grammatical rules except that they may not at any point make reference to semantic matters. For natural languages this is hard to do, but languages can be devised for which this can be done, e.g. that of Principia Mathematica.

Section 3 - Transformation Rules

Transformation rules determine how from given sentences we may infer others. The totality of transformation rules for a language S determines the relation of "direct consequence in S". A sentence C is a consequence of a set of sentences P in S if it can be obtained by a chain of transformations from the sentences in P.

Thus, formation rules correspond to grammar and transformation rules correspond to logic, both of which have a purely formal character. The word "sentence" is preferred to "proposition" because of the concern for syntax rather than semantics.

Section 4 - Syntactical Terms

"term" here means "concept". The terms "sentence" and "direct consequence" are primitives which may be used to define the other syntactical terms of interest in logical syntax.

"true" and "false" cannot be defined syntactically, but where a sentence is true or false "only by reason of rules of the language" then it is termed valid or contravalid respectively. A sentence A is valid if it is a consequence of the null class of premises, and is contravalid if every sentence of the language is a consequence of A. A sentence is determinate if it is either valid or contradictory and indeterminate otherwise.

Section 5 - L-terms

L-rules are rules of a purely logical character. A system may include rules which are not L-rules (e.g. rules expressing laws of physics) which are called P-rules.

C is an L-consequence of P if it is derivable from P using only L-rules. If C is a consequence but not an L-consequence, then it is a P-consequence. Other L- and P- terms may be defined analogously, e.g. a sentence is L-valid or analytic if it is an L-consequence of the null class of premises. Similarly L-contravalid or contradicatory, L-determinate (analytic or contradictory), L-indeterminate or synthetic.

The totality of sentences may be shown thus:

L-validP-valid P-contravalidL-contravalid

Section 6 - Content

The class of non-valid consequences of a sentence is called the content of the sentence. The content of a sentence represents its sense (excluding psychological connotations).

Two sentences are called equipollent if they have the same content.

Two expressions are called mutually synonymous if the content of any sentence containing one of them is not changed if we replace that expression by the other.

Section 7 - Pseudo-Object-Sentences

The task of "syntax" is to analyse given sentences, proofs or theories in the above terms. The results of such an analysis should be formulated as syntactical sentences, e.g. "such and such a sentence contained in a certain theory is synthetic, but a certain other sentence is merely analytic," or: "This particular word of such a theory is synonymous, but not L-synonymous, with that and that combination of words", etc. However, many properly philosophical sentences are not apparently about syntax.

Sentences containing irreducible references to not syntactic objects are called real object-sentences. There is another class of sentences which are like object-sentences in their form but like syntactical sentences in their content. These are called pseudo-object-sentences.

Next there is an explanation of how pseudo-object-sentences can be recast in a way which makes it clear that their content is syntactic. I'm afraid this doesn't hang together for me so I can't do a precis.

Section 8 - The Material and The Formal Modes of Speech

We now have three kinds of sentence, real-object, pseudo-object, and syntactical. Empirical science contains propositions of the first kind, and philosophy of the second and third kinds, which differ in their mode of expression rather than their content, which in both cases is syntactical.

This difference in mode of expression is designated by the phrases material mode of speech and formal mode of speech. In the former there are apparent references to real objects, in the latter these are not present or have been eliminated. e.g. "The morning star and the evening star are identical." is in the material mode, and can be translated into the formal mode as "The words 'evening star' and 'morning star' are synonymous".

Sentences in the material mode are deceptive in that they appear to refer to real objects but do not really do so. Most of the statements of philosophy are of this kind.

Lecture III - Syntax as The Method of Philosophy

Section 1 - The Material Mode of Speech

The question to answer is:
  • What is logical analysis?
  • What kind of sentences are those that express the results of logical analysis?
    (these seem to be considered one question)
    The answer is: "syntactical sentences", and hence philosophy is the application of the syntactical method.

    A lot of philosophical confusion results from the deceptive form of syntactical sentences expressed in the material mode. Idle philosophical controversies can be resolved by translating these confusing theses into the formal mode.

    Often the material mode involves reference to abstract objects such as numbers. Statements about such abstract entities can be replaced by statements which are about the kind of syntactic object used to refer to them. e.g. "7 is a number" can be translated into "'7' is a numerical sign". This process can be adapted to all kinds of abstract object.

    Similarly, talk about meanings (which are themselves abstract objects) can be translated into the syntactical analogues of semantic terms, such as equipollent and synonymous.

    By these means logical analysis will be able to convert logical statements into purely syntactic forms, permitting their status to be established by syntactical methods. Of course this doesn't apply to the real-object statements of the empirical sciences.

    Section 2 - Modalities

    Modality sentences are in fact veiled syntactical sentences, namely sentences of the material mode of speech. "That A is older than B, and B is older than A, is an impossible state." can be translated into the formal mode as "The sentence 'A is older than B, and B is older than A' is contradictory".

    Similar considerations apply to physical as well as logical modalities. e.g. "The state of a particular solid iron ball swimming on the water is a physical impossibility" can be translated as "The sentence 'This solid iron ball is swimming on the water' is contravalid" (actually P-contravalid).

    In general modal sentences are expressed in the material mode and can be translated into the formal mode using the following table:

    ModalityParallel syntactical terms
    termsL-termsGeneral terms
    log. or phys. impossiblecontradictorycontravalid
    log. or phys. possiblenon-contradictorynon-contravalid
    log. or phys. necessaryanalyticvalid
    log. or phys. contingentsyntheticindeterminate

    Section 3 - Relativity in Regard to Language

    Since, as this method makes clear, philosophical statements are about language it is clear that their truth will depend upon which language they are about. Translation into the formal mode makes it more conspicuous that a reference to the language under consideration is necessary, and this enables some kinds of philosophical confusion to be remedied.

    For example, a dispute between Russell and Hilbert about what numbers are, can be seen to be spurious since on translation their relative claims can be seen to be claims about what numbers are in distinct formal languages, and the claims are therefore not incompatible.

    Section 4 - Pseudo-questions

    Use of the material mode of expression, while not incorrect in itself, can lead one into making statements which are not real-object statements but cannot be translated into the formal mode. These statements are metaphysical pseudo-questions, e.g. whether numbers are real objects or ideal objects.

    It is advisable therefore to use the material mode with caution and to translate back into the formal mode at key points in discussion. Faced with someone unwilling to undertake this kind of explication, withdrawing from the debate may be the best policy.

    Section 5 - Epistemology

    The properly philosophical part of epistemology includes the logical analysis of the verification of assertions. Questions of this kind can be expressed in the formal mode, since they are concerned with the observation sentences which are deducible from the assertion in question.

    Hence epistemology - (as philosophy) - is a part of syntax.

    Section 6 - Natural Philosophy

    Natural Philosophy is the syntactic analysis of the language-system of science.

    Section 7 - What Physicalism Asserts

    The physical language of science is that in which we speak about physical things in everyday life or in physics.

    The physical language of science is a universal language comprehending the contents of all other scientific languages.

    Every sentence of any branch of science is equipollent to some sentence of the physical language.

    Section 8 - What Physicalism Does not Assert

    Physicalism asserts an equipollence between sentences, it does not assert identity or equivalence of any other kind of entity, e.g. correspondence between mental states and physical states.

    Section 9 - The Unity of Science

    Closely associated with physicalism is the doctrine of the unity of science, which asserts that there are no logical distinctions to be drawn between the different branches of science, which share the same fundamental physical language in which their theories can be expressed.

    Syntactically: the terms of all branches of science are logically uniform.

    The method of logical syntax, that is, the analysis of the formal structure of language as a system of rules, is the only method of philosophy.

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