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Quine's lectures on Carnap's Philosophy of Logical Syntax
Quine gave three lectures on Carnap's Philosophy of Logical Syntax at Harvard in 1934. The first of these lectures provided the basis for the paper Truth by Convention [Quine36].
A few words placing the lectures in historical context.
Quine's first lecture addresses primarily the concept of analyticity and also the a priori, not professing to be an account of Carnap's philosophy, but rather as providing introductory background prior to an account of Carnap's philosophy of logical syntax in the second and third lectures.
On Carnap's syntactic methods and the method of arithmetisation.
Here Quine tells the story of how these syntactic methods are to transform philosophy.
A few words placing the lectures in historical context.

On completing his doctoral dissertation (in just two years) Quine obtained a Sheldon Travelling Fellowship (for one year) and went to Vienna in the fall of 1932. Carnap had then taken up a position in Prague, so after attending lectures by Schlick in Vienna Quine went on to Prague in the spring, meeting Carnap in March 1933. Carnap was then writing Logische Syntax Der Sprache [Carnap34], and Quine had the opportunity to read the book as it was typed up by Ina Carnap.

Quine's reservations about the analytic/synthetic distinction date from this first acquaintance with Carnap's work.

Quine was elected a junior fellow of Harvard while in Europe. His doctoral dissertation was being prepared for publication, but Quine's European travels resulted in his wishing to make substantial changes, the completion of which occupied the greater part of his time during the first year of his three year fellowship. He was also asked to prepare three lectures on the philosophy of Carnap, which were delivered in November 1934.

Lecture I: The A Priori
Quine's first lecture addresses primarily the concept of analyticity and also the a priori, not professing to be an account of Carnap's philosophy, but rather as providing introductory background prior to an account of Carnap's philosophy of logical syntax in the second and third lectures.
Definitions of Analyticity and the A Priori

This lecture is devoted to a discussion of "the analytic character of the a priori". Quine begins by reference to Kant, citing first Kants view that analytic judgements are a proper subset of the a priori, and quoting the definition of a priori as having "the character of inward necessity". "and holds independently of any possible experience".

He provides multiple characterisations of (or claims about) analyticity as follows:

  1. a judgement the truth of which can be established directly by analysis of the concepts involved
  2. an analytic judgement can do no more than call our attention to something already contained in the definitions of our terms
  3. consequences of definitions, conventions as to the uses of words
  4. consequences of linguistic fiat
and observes that among them "are to be reckoned" logic and "the bulk, at least" of mathematics.

Quine then notes Kant's view that there are judgements which are synthetic but a priori (e.g. those of geometry), and the more recent grounds for rejecting this claim (by showing that the whole of mathematics, including geometry, is analytic), and the doctrine that all a priori judgements are analytic. To examine this claim Quine proposes to examine in detail "the nature of the analytic".


On the face of it the first item is offered as a definition and subsequent items are clarifications, but these by no means follow. Possibly his intention is that we should read them conjointly as defining the concept.


Quine begins by distinguishing two kinds of definition, explicit definitions, which are "merely a convention of abbreviation", and implicit definitions, which are sets of rules specifying that certain sentences in which the word (say 'K') being defined occur and which are to be accepted by convention as true, "their truth constitutes the meaning of 'K'". Quine observes that definitions have often been construed as exclusively of the kind he calls "explicit", but that it is convenient in the present context to adopt the broader usage (noting that there is precedent for it).

Quine then tells us that analyticity depends on (nothing more than) definitions. This leads to an extended expansion of his explanation of analyticity based around examples of how this process of defining a language might proceed.


Note first that Quine's canonical notion of definition, his "explicit" definitions, are syntactic in character, they are syntactic abbreviations, and Quine does not appear here to have a notion of definition as assigning meaning to or denotation for a new name.

Note also that Quine does not mention here that his explicit definitions are eliminable, whereas his implicit definitions may not be.

It may be helpful to consider to what extent Quine's arguments depend upon his particular conception of definition and to what extent the arguments remain sound if we adopt, for example, a conception of definition as introducing a new name (constant) by conservative extension to an existing language or theory.

Quine's conception of analyticity makes it dependent not on meanings, but on definitions. This conception he applies to natural languages not merely to formally defined languages, so one might get the impression that analyticity only arises in natural languages once the language has been partly or wholly augmented by definitions of the words of the language.

This makes Quine's conception of analyticity dependent on a process of formalisation which is potentially more problematic than the identification of analytic sentences in natural languages on unmediated operation of our intuitions about their meaning, without the need to deliver definitions of all the terms involved.

The cases in which the concept is most readily applicable are those in which a sentence in a natural language is considered in which there is no significant difficulty of comprehension, or a sentence in a formal language whose subject matter is straightforward and whose semantics can be presented unambiguously (for example the first order language of arithmetic). Quine's subsequent explication of the idea of analyticity through a process of providing definitions for terms originating in a natural language is the least plausible context for a successful outcome.

Lecture II: Syntax
On Carnap's syntactic methods and the method of arithmetisation.
Formally Describing Languages using Syntactic Rules
Semantics and Syntax

Quine begins with a discussion of the meaning of the word "semantic", which apparently was then in use not only by Pierce to talk about menaing, but aslo by Chistwick in a sense which embraced syntax. Quine presents Carnap's use of the term "syntax" as a means of avoiding this ambiguity in the term "semantic".

Kinds of Rules

We next hear that Carnap divides his rules of syntax into two kinds rules of formation and of transformation. The formation rules are concerned with grammar and tell us what are the meaningful sentences.

Formation Rules

Quine notes the complexity of a full account of the formation rules for natural languages and cites this as the reason why Carnap choses an artificial language as object for syntactic study. He then goes on to describe the formation rules for an artificial language, somewhat, but not entirely, like the one used by Carnap.

Transformation Rules

The transformation rules "specify the conditions under which a sentence may be inferred". They "answer to" what Quine described in his first lecture as implicit definitions. Quine replays the formal system from the first lecture, which covers the propositional calculus and unspecified other areas, offering these as examples of transformation rules (among which he appears to include axiom schemata).

Defining the Simple System
Formation Rules

Quine gives a lightweigh description of a simple language similar to one formally defined by Carnap.

The formation rules are rules governing how sentences may be constructed. This involves primitive symbols (not defined, or given implicit definitions), a range of defined logical or mathematical operators, and various descriptive operators which permit the construction of empirical sentences.

Since explicit definitions are regarded as syntactic abbreviations, they fall under the heading of formation rules.

The formation rules define the notion of sentence for the language in question.

Transformation Rules

The purpose of the transformation rules is to infer rather than to construct sentences, and they serve as implicit definitions of the primitive symbols, However, Quine says we can go as far as we like with these transformation rules, "Where we stop in this process is an arbitrary matter to be decided by pragmatic considerations" (i.e. not confined to what would normally be considered definition?).

The transformation rules define a relation of immediate consequence between sets of sentences (the premises) and sentences (the conclusion).

Quine's Blurring of Consequence

Quine confesses that he is blurring over the distinction in Carnap between to difference kinds of transformation rule, those defining consequence and those defining deducibility. The relation which Quine is calling consequence is Carnap's derivability, Quine claims.

The divergence with Carnap is worse than Quine admits in that case. Carnap has a set of d-terms which arise from the notion of derivability and a set of c-terms which arise from the broader notion of consequence (which is are syntactic surrogates for semantic properties). Most of the derived notions mentioned by Quine are defined in terms of consequence, not in terms of derivation, i.e. they are c-terms, not d-terms as Quine seems to be suggesting.

Derivative Notions

Various derivative notions then become definable for each language in terms of the notions of sentence and immediate consequence.

These include:

  • analytic - a sentence which is a consequence of every sentence
  • contradictory - a sentence of which every other sentence is a consequence
  • synthetic - a sentence which is neither analytic nor contradicatory
  • syntactic category - a group of syntactically interchangeable expressions, salva well-formedness
  • synonymity - symbols whose interchange yields mutually derivable sentences
  • content - the set of non-analytic consequences of a sentence

Quine makes a particular point of the arbitrary nature of analytic truth here stating that "it is a matter of linguistic convention what truths turn out to be analytic and what ones do not, it depends how we frame our definitions".

Truth of Synthetic Propositions
Page 79 last para. Quine here says "in fact, the separation of synthetic proposition into into true and false cannot be carried out at all within a more formally syntactic approach such as I am now engaged in". And generally, I have found no mention in Quine of Carnap's P-rules the purpose of which is to formulate empirical scientific laws or facts.
Arithmetisation of Syntax
Quine provides a sketch of the method of arithmetisation used by Carnap to formalise the syntactic concepts in his language (at least, the d-concepts, though Quine doesn't go into that).
Lecture III: Philosophy as Syntax
Here Quine tells the story of how these syntactic methods are to transform philosophy.
Recap of General Background
the recap

Quine begins with the "expository fiction" that we have to hand that collection of sentences which we accept as true and are embarking on the construction of an explicit formalization of the language.

This is to be a set of implicit and explicit definitions consistent with the past usage represented by the set of accepted truths.

We are reminded that this process can go as far as we find convenient, and that how far we go determines the extent to which the analytic is extended "at the expense of the synthetic".

Some commentary

We are reminded here that the process involves making a choice about which sentences are to be analytic, and that as we do so we add rules the effect of which is to render analytic sentences which had hitherto been synthetic.

I don't think that this is the way in which Carnap saw the process.

The main bulk of the definitions of the transformation rules is in lock-step with additions to the formation rules, since it is done by explicit definitions which introduce new constants and give explicit values for those constants. This does not result in the reclassification of sentences which were previosly synthetic as analytic, but rather introduces new sentences of which those which are true are analytic truths.

Carnap's definition of synthetic truth is clearly framed in the expectation that abstract entities are defined completely (explicitly, except for the few primitive logical constants) on introduction of the terms, so that there are no sentences only involving abstract entities which are synthetic.

Synthetic sentences only appear when descriptive constants are introduced. Primitive descriptive constants are given P-rules rather than L-rules as implicit "definitions", though it is more appropriate to think of these as fundamental physical laws than as definitions, and there are therefore no new analytic sentences except those involving only vacuous occurrences of those new constants. Non-primitive descriptive constants are defined explicitly in terms of primitive descriptive constants, This will introduce new analytic and new synthetic truths, but only truths which are mere abbreviations of previously available analytic or synthetic truths. This does not result in any reclassifications of sentences.

Quine's explanatory fiction is widely out of line with any reasonable approach to formalising the language of mathematics and science, and is very misleading in its suggestion that the epistemic status of sentences is arbitrarily selected.

Quine's Concern in this Lecture
In a single paragraph (top of page 88) Quine gives an illuminating concise statement of what is concerned with in the third of his lectures, which I will precis here, and comment on.

Quine first remarks that in our general thinking "we seem invariably" to come against non-empirical philosophic problems which cannot permanently be "swept aside", If philosophy is syntax then we must either solve these problems using syntactic methods or throwing them out as illusory meaningless questions.

He proposes to test whether philosophy as syntax is a constructive or a "merely negative" doctrine by showing in detail how these problems appear when approached from the syntactic viewpoint.


Quine has laid the ground here for an critique of Carnap's method along the lines that it rejects as meaningless substantive philosophical problems.

In the context of Quine's own account of the method so far it is hard to see how such a criticism could be established, for Quine has made it appear that Carnap's method can be used to bring into the syntactic fold pretty much any problem at all, by putting forward rules which render analytic whatever answer may be preferred.

If however, one takes seriously (despite Quine not having even mentioned these constraints), that L-rules should serve only to capture the meanings of the terms introduced, and that any synthetic facts or laws should be expressed by P-rules (which Quine has not mentioned) which in turn should be empirically based, then there might be the possibility of a criticism for failure to address some problem in metaphysics.

The constraint of L-rules to meaning is hard to maintain however at this stage in the development of Carnap's philosophy, it is more arguable that it is a weakness at this stage that that constraint is not presented, leaving open the criticism that the syntactic methods allow the arbitrary misclassification of synthetic propositions as logical truths.

Syntactic and Quasi Syntactic properties

Quine now addresses what may be thought the core of Carnap's Logical Syntax via the ideas of syntactic and quasi syntactic properties, and the way in which talk of semantic notions such as meaning can be replaced by talk about syntactic properties.


I have the impression here, for the first time in these lectures, that Quine really is onboard, and really does like elimination of concepts such as "meaning" in favour of syntactic properties, at pretty much every stage hitherto I see Quine as giving qualified assent, or even as (possibly unwittingly) offering a caricature.

Sadly, for the possibility of a rapprochement, these are the very elements of Carnap's Logical Syntax which are discarded when Carnap (possibly under the influence of Quine's critique both here and in "Truth by Convention") moved on from Logical Syntax to embrace semantics, and thence admit abstract entities in a wholehearted pragmatic (rather than metaphysical) way. (Arguably this is needed to make clear the character which L-rules must have and thereby defend against the suggestion by Quine that the formulation of L-rules arbitrarily reclassifies synthetic sentences as analytic.)

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