Carnap-Ramsey sentences
Encyclopedia
In philosophy
, Ramsey sentences refer to an attempt by logical positivist philosopher Rudolf Carnap
to reconstruct theoretical proposition
s such that they gained empirical content.
For Carnap, questions such as: “Are electron
s real?” and: “Can you prove electrons are real?” were not legitimate questions implying great philosophical/metaphysical
import. They were meaningless "pseudo-questions without cognitive content,” asked from outside a language framework of
science. Inside this framework, entities such as electrons or sound waves, and relations such as mass
and force
not only exist and have meaning, but are "useful" to the scientists who work with them. To accommodate such internal questions in a way that would justify their theoretical content
empirically – and to do so while maintaining a distinction between analytic and synthetic propositions – Carnap set out to develop a systematized way to consolidate theory and empirical observation in a meaningful language formula.
Carnap began by differentiating observable things from non-observable things. Immediately, a problem arises: neither the German
nor the English language
naturally distinguish predicate terms on the basis of an observational categorization. As Carnap admitted, "The line separating observable from non-observable is highly arbitrary." For example, the predicate "hot" can be perceived by touching a hand to a lighted coal. But "hot" might take place at such a microlevel (e.g., the theoretical "heat" generated by the production of proteins in a eukaryotic cell) that
it is virtually non-observable (at present). Physicist-philosopher Moritz Schlick
characterized the difference linguistically, as the difference between the German verbs "kennen" (knowing as being acquainted with a thing – perception) and "erkennen" (knowing as understanding a thing – even if
non-observable). This linguistic distinction may explain Carnap’s decision to divide the vocabulary into two artificial categories: a vocabulary of non-observable ("theoretical") terms (hereafter "VT"): i.e., terms we know of but are not acquainted with (erkennen), and a vocabulary of observable terms ("VO"), those terms we are acquainted with (kennen) and will accept arbitrarily. Accordingly, the terms thus distinguished were incorporated into comparable sentence structures: T-terms into Theoretical sentences (T-sentences); O-terms into Observational sentences (O-sentences).
The next step for Carnap was to connect these separate concepts by what he calls "Correspondence Rules" (C-rules), which are "mixed" sentences containing both T- and O-terms. Such a theory can be formulated as: T + C = df: the conjunction of T-postulates + the conjunction of C-rules – i.e.,
. This can be further expanded to include class terms such as for the class of all molecules, relations such as "betweenness," and predicates: e.g., TC ( t1, t2, . . ., tn, o1, o2, . . ., om). Though this enabled Carnap to establish what it means for a theory to be "empirical," this sentence neither defines the T-terms explicitly nor draws any
distinction between its analytic and its synthetic content, therefore it was not yet sufficient for Carnap’s purposes.
In the theories of Frank P. Ramsey
, Carnap found the method he needed to take the next step, which was to substitute variables for each T-term, then to quantify existentially all T-terms in both T-sentences and C-rules. The resulting "Ramsey sentence" effectively eliminated the T-terms as such, while still providing an account of the theory’s empirical content. The evolution of the formula proceeds thus:
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, Ramsey sentences refer to an attempt by logical positivist philosopher Rudolf Carnap
Rudolf Carnap
Rudolf Carnap was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism....
to reconstruct theoretical proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s such that they gained empirical content.
For Carnap, questions such as: “Are electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s real?” and: “Can you prove electrons are real?” were not legitimate questions implying great philosophical/metaphysical
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
import. They were meaningless "pseudo-questions without cognitive content,” asked from outside a language framework of
science. Inside this framework, entities such as electrons or sound waves, and relations such as mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
not only exist and have meaning, but are "useful" to the scientists who work with them. To accommodate such internal questions in a way that would justify their theoretical content
empirically – and to do so while maintaining a distinction between analytic and synthetic propositions – Carnap set out to develop a systematized way to consolidate theory and empirical observation in a meaningful language formula.
Carnap began by differentiating observable things from non-observable things. Immediately, a problem arises: neither the German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
nor the English language
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
naturally distinguish predicate terms on the basis of an observational categorization. As Carnap admitted, "The line separating observable from non-observable is highly arbitrary." For example, the predicate "hot" can be perceived by touching a hand to a lighted coal. But "hot" might take place at such a microlevel (e.g., the theoretical "heat" generated by the production of proteins in a eukaryotic cell) that
it is virtually non-observable (at present). Physicist-philosopher Moritz Schlick
Moritz Schlick
Friedrich Albert Moritz Schlick was a German philosopher, physicist and the founding father of logical positivism and the Vienna Circle.-Early life and works:...
characterized the difference linguistically, as the difference between the German verbs "kennen" (knowing as being acquainted with a thing – perception) and "erkennen" (knowing as understanding a thing – even if
non-observable). This linguistic distinction may explain Carnap’s decision to divide the vocabulary into two artificial categories: a vocabulary of non-observable ("theoretical") terms (hereafter "VT"): i.e., terms we know of but are not acquainted with (erkennen), and a vocabulary of observable terms ("VO"), those terms we are acquainted with (kennen) and will accept arbitrarily. Accordingly, the terms thus distinguished were incorporated into comparable sentence structures: T-terms into Theoretical sentences (T-sentences); O-terms into Observational sentences (O-sentences).
The next step for Carnap was to connect these separate concepts by what he calls "Correspondence Rules" (C-rules), which are "mixed" sentences containing both T- and O-terms. Such a theory can be formulated as: T + C = df: the conjunction of T-postulates + the conjunction of C-rules – i.e.,
. This can be further expanded to include class terms such as for the class of all molecules, relations such as "betweenness," and predicates: e.g., TC ( t1, t2, . . ., tn, o1, o2, . . ., om). Though this enabled Carnap to establish what it means for a theory to be "empirical," this sentence neither defines the T-terms explicitly nor draws anydistinction between its analytic and its synthetic content, therefore it was not yet sufficient for Carnap’s purposes.
In the theories of Frank P. Ramsey
Frank P. Ramsey
Frank Plumpton Ramsey was a British mathematician who, in addition to mathematics, made significant and precocious contributions in philosophy and economics before his death at the age of 26...
, Carnap found the method he needed to take the next step, which was to substitute variables for each T-term, then to quantify existentially all T-terms in both T-sentences and C-rules. The resulting "Ramsey sentence" effectively eliminated the T-terms as such, while still providing an account of the theory’s empirical content. The evolution of the formula proceeds thus:
- Step 1 (empirical theory, assumed true): TC ( t1 . . . tn, o1 . . . om)
- Step 2 (substitution of variables for T-terms): TC (x1 . . . xn, o1 . . . om)
- Step 3 (
-quantification of the variables): 
.
Step 3 is the complete Ramsey sentence, expressed "RTC," and to be read: "There are some (unspecified) relations such that TC (x1 . . . xn, o1 . . . om) is satisfied when the variables are assigned these relations. (This is equivalent to an interpretation as an appropriate model: there are relations r1 . . . rn such that TC (x1 . . . xn, o1 . . . om) is satisfied when xi is assigned the value ri, and
.)
In this form, the Ramsey sentence captures the factual content of the theory. Though Ramsey believed this formulation was adequate to the needs of science, Carnap disagreed, with regard to a comprehensive
reconstruction. In order to delineate a distinction between analytic and synthetic content, Carnap thought the reconstructed sentence would have to satisfy three desired requirements:- The factual (FT) component must be observationally equivalent to the original theory (TC).
- The analytic (AT) component must be observationally uninformative.
- The combination of FT and AT must be logically equivalentLogical equivalenceIn logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...
to the original theory – that is,
.
Requirement 1 is satisfied by RTC in that the existential quantification of the T-terms does not change the logical truthLogical truthLogical truth is one of the most fundamental concepts in logic, and there are different theories on its nature. A logical truth is a statement which is true and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement.Logical...
(L-truth) of either statement, and the reconstruction FT has the same O-sentences as the theory itself, hence RTC is observationally equivalent to TC : (i.e., for
every O-sentence: O,
). As stated, however, requirements 2 and 3 remain unsatisfied. That is, taken individually, AT does contain observational information (such-and-such a theoretical term is observed to do such-and-such, or hold such-and-such a relation); and AT does not necessarily follow from FT.
Carnap’s solution is to make the two statements conditional. If there are some relations such that [TC (x1 . . . xn, o1 . . . om)] is satisfied when the variables are assigned some relations, then the relations assigned to those variables by the original theory will satisfy [TC (t1 . . . tn, o1 . . . om)] – or: RTC → TC. This important move satisfies both remaining requirements and effectively creates a distinction between the total formula’s analytic and synthetic components. Specifically, for requirement 2: The conditional sentence does not make any information claim about the O-sentences in TC, it states only that "if" the variables in are satisfied by the relations, "then" the O-sentences will be true. This means that every O-sentence in TC that is logically implied by the sentence RTC → TC is L-true (i.e., every O-sentence in AT is true or not-true: the metal expands or it does not; the chemical turns blue or it does not, etc.). Thus TC can be taken as the non-informative (i.e., non-factual) component of the statement, or AT. Requirement 3 is satisfied by inference: given AT, infer FT → AT. This makes AT + FT nothing more than a reformulation of the original theory, hence AT Ù FT
ó TC.
Finally, the all-important requirement for an analytic–synthetic distinction is clearly met by using two distinct processes in the formulation: drawing an empirical connection between the statement’s
factual content and the original theory (observational equivalence), and by requiring the analytic content to be observationally non-informative. Of course, Carnap’s reconstruction as it is given here is not intended to be a literal method for formulating scientific propositions. To capture what Pierre DuhemPierre DuhemPierre Maurice Marie Duhem was a French physicist, mathematician and philosopher of science, best known for his writings on the indeterminacy of experimental criteria and on scientific development in the Middle Ages...
would call the entire "holistic" universe relating to any specified theory would require long and complicated renderings of RTC → TC. Instead, it is to be taken as demonstrating logically that there is a way that science could formulate empirical, observational explications of theoretical concepts – and in that context the Ramsey and Carnap construct can be said to provide a formal justificatory
distinction between scientific observation and metaphysical inquiry. The Ramsey and Carnap formulation is, of course, not inviolate. Among its critics are John Winnie, who extended the requirements to include an
"observationally non-creative" restriction on Carnap’s AT – and both Quine and Hempel attacked Carnap’s initial assumptions by emphasizing the
ambiguity that persists between observable and non-observable terms. Nonetheless, the Ramsey and Carnap construct was an interesting attempt to draw a substantive line between science and metaphysics.
Works cited
- Carnap, R. "Theoretical Concepts in Science," with introduction by Psillos, S. Studies in History and Philosophy of Science Part A
- Carnap, R. (1966) An Introduction to the Philosophy of Science (esp. Parts III, and V), ed. Martin Gardner. Dover Publications, New York. 1995.
- Carnap, R. (1950) "Empiricism, Semantics, and Ontology," in Moser & Nat, Human Knowledge Oxford Univ. Press. (2003).
- Demopoulos, W. "Carnap on the Reconstruction of Scientific Theories," The Cambridge Companion to Carnap, eds. R. Creath and M. Friedman.
- Moser, P.K. and vander Nat, A. (2003) Human Knowledge Oxford Univ. Press.
- Schlick, Moritz (1918) General Theory of Knowledge (Allegemeine Erkenntnislehre). Trans. Albert Blumberg. Open Court Publishing, Chicago/La Salle, IL. (2002).
- Hallvard Lillehammer, D. H. Mellor (2005), Ramsey's legacy, Oxford University Press, pg 109.
- Stathis Psillos, "CARNAP, THE RAMSEY-SENTENCE AND REALISTIC EMPIRICISM", 2000
External links