Paper and the Author:

Rudolf Carnap, born in 1891 in Germany, was an influential figure in 20th-century analytic philosophy, known for his contributions to logical empiricism and the Vienna Circle. He has also contributed to semantics, logical syntax, and philosophy of science, among others.

Rudolph Carnap was a Philosophy Professor mostly at UCLA.

Here is the full article: Empiricism, Semantics, and Ontology

Background and Key Concepts:

Empiricism (Views vary; Carnap is a type of empiricist) is a philosophical approach emphasizing sensory experience and empirical evidence in knowledge formation. Empiricists believe that all or most knowledge originates from sensory perception, and they argue that meaningful understanding and justified beliefs are derived from observation, experimentation, and sense data. This perspective contrasts with rationalism, which posits that reason and innate ideas are primary (all or most) sources of knowledge.

Linguistic Framework is a set of rules and conventions concerning the use of language that one posits and accepts. These rules establish the meanings of terms, the criteria for meaningful statements, and the conditions under which propositions can be judged true or false. Different frameworks can vary widely depending on their purposes, goals, and the linguistic rules they adopt.

Internal Questions are questions regarding entities’ existence or true/false judgments that are determined analytically within the bounds of a framework. For instance, we may ask whether an entity X is compatible with the framework. The answer to the internal question is answered by logical and/or empirical means, depending on the nature of the framework. For instance, a mathematics framework would have logical methods, but a psychology framework would require investigating empirical behaviors.

External Questions are questions about the existence of the system constructed by the framework. According to Carnap’s view, the question is not metaphysical but pragmatical. I.e., the question concerns whether one should adopt the framework for its fruitfulness. In this view, we may think that the reality of the framework consists in our use of it (I.e., a framework comes to life because it is useful). For the external questions, we may compare different frameworks. Concerning mathematics (perhaps the two frameworks have different axioms), is Framework One better than Framework Two?

The Aim of Carnap’s Paper:

In “Empiricism, Semantics, and Ontology,” Carnap attempts to show how our languages refer to abstract entities and are compatible with empiricism by treating them as logical consequences of a linguistic framework one posits and adopts. The paper addresses some relevant questions like “How should we consider the place of abstract entities in our language (e.g., concepts and numbers),” and “What is the role of abstract entities?”

Why does the paper matter?
Think of it as solving a puzzle about how it is possible to talk about things we can’t see or touch (like justice and numbers) without abandoning a scientific approach that values evidence and observation.

Carnap’s thesis is that empiricism is compatible with how our languages refer to abstract entities.

Paper Reconstruction:

In semantic theory, some hold that certain expressions refer to certain entities, concrete or abstract. Empiricists avoid referring to abstract entities since they do not believe they exist. However, it is a challenge to do mathematics and natural science without seeming to refer to abstract entities like infinity, colors, and quarks. How may empiricists speak of and accept abstract entities without committing to the existence of abstract entities? Carnap attempts to provide a solution.

There are internal and external questions (see definitions above) regarding the existence or reality of entities. Carnap provides an example of the framework of “The world of things,” encompassing ordinary mid-size objects like tables and chairs. Suppose we have accepted the framework. The answers to internal questions like “Is that chair brown,” “Is that table shorter than that chair,” or “Can that table fly?” must be answered within the rules of the framework. In this case, the rule would specify that the answer to the question depends on observation. The answer to the preceding questions is ‘yes’ if observations confirm it. On the other hand, the external question asks whether one should accept the framework, for instance, “The world of things” in the first place. 1

Concerning the external question, some philosophers are interested in the status of abstract entities – for example, whether numbers have a metaphysical characteristic called reality. They are skeptical of accepting entities with dubious existential status; thus, they often answer the external question negatively. I.e., one is unjustified in accepting a framework with unjustified abstract entities. However, Carnap dismisses their concerns. He states they have yet to articulate their external questions using scientific terminology and have not provided meaningful cognitive content (i.e., Their external question and concern lacks substance). Then how should one answer the external question? Carnap argues that one should accept, for instance, the “The world of things” framework based on its fruitfulness or utility. Moreover, he asserts that positing a new framework requires no theoretical justification because it does not entail the expression of beliefs, assumptions, or assertion of the reality of the entities within the framework.

The following is the example of framework construction:

The System of Propositions:2
(1) Introduction of a name:

Name: Propositions

(2) Introduction of a variable:

Variables p, q, etc., where substituting any sentence with a truth value is allowed.
For instance, we may substitute “Spotify has more subscribers than Apple Music on 2/14/2024” for p.

(3) Introduction of rules (at least one):

“For every p, either p or ¬p.”
“There is a p such that p is not necessary and ¬p is not necessary.”

Let’s apply the simple rules.
Suppose that p stands for “It is raining.”
Then we have:

p: It is raining.
¬p: It is not raining

Let’s examine the conditions:

  • p is not necessary” translates to “It is raining is not necessary.” This comes out true because there are circumstances where it may or may not be raining.
  • ¬p is not necessary” translates to “It is not raining is not necessary.” This also yields true because there are situations where it may or may not be the case that it’s not raining.

So, in this example, since p is not equivalent to not-p and “There is a p such that p is not necessary and not-p is not necessary” holds true, p is true according to this simple framework.

Finally, semantical analysis often involves attributing certain expressions in a language to refer to extra-linguistic (outside language) entities. While referring to physical things or events poses no issue, objections arise regarding the designation of abstract entities (properties, numbers, or propositions). The controversy of the status of abstract entities still needs to be solved, as philosophers hold opposing views without common ground on relevant evidence to settle the dispute. However, Carnap holds that the existence of abstract entities is seen as a pseudo-question until a shared understanding and question regarding abstract entities are developed. According to his framework, while internal assertions require evidence, accepting a system of entities doesn’t necessarily entail belief or assertion. I.e., the contents of the framework are only syntactically expressable and thus useful, but they do not make ontological commitments. Therefore, his framework is a solution to the compatibility of abstract entities and empiricism. So he argues.

A Critical Note:

One of the issues I have been grappling with is how much control we have over the linguistic framework we adopt. We may choose the names and content of a language, but we may not have any say on its logical structure or how contents logically relate to each other. Consequently, intelligibility and any sense of fruitfulness are entailed in the metaphysical or logical possibility, so our choices are not mere conventions. Here, I use metaphysical possibility in the sense that it is possible for human cognition. There could be other possibilities nonhumans may grasp. For instance, suppose the following is true: We can give ‘five’ any other name or symbol, but we can only metaphysically represent quantities with the concept of numbers. Then, we do not choose a specific framework in certain domains because it is practical but because it is the only intelligible, metaphysical possibility. If so far correct, the external question must be grounded in metaphysical or logical constraints; therefore, we cannot be neutral regarding abstract entities we cognize, at least in some domains.

On the other hand, others suggest that even within a given set of metaphysical possibilities, we can still choose the most productive options. I am left pondering whether Carnap’s viewpoint holds some truth, and I am curious about our capacity to select regarding framework acceptance. Furthermore, what about those who argue that language is more flexible than we give it credit and that we can create new logical structures and frameworks that allow for different ways of thinking about abstract entities? It is true that we can develop different mathematics based on different axioms. Science has also changed dramatically, positing different entities to explain natural phenomena. As Carnap suggests, entities within the framework have meaning, and entities relate to one another; thus, we can have an intelligible conversion, for instance, about physics, without making realist claims about quarks. So Carnap’s objections are far from trivial when considering the nature of math and science; they must be taken seriously.


  1. Carnap, on page 24, provides a parallel example (framework for the “system of numbers”) of internal and external questions that are logical in nature. ↩︎
  2. See page 28 for more examples (The system of thing properties, The system of integers and rational numbers, The system of real numbers, and The spatiotemporal coordinate system for physics) ↩︎


  • Carnap, Rudolf. “Empiricism, Semantics, and Ontology.” Revue Internationale de Philosophie, vol. 4, no. 11, 1950, pp. 20–40.

*Disclaimer: This article is a creative interpretation and synthesis work, drawing inspiration from multiple sources. While efforts have been made to ensure the accuracy of the information presented, readers are encouraged to consult the source material for a comprehensive understanding.

**Please note that I often write the Critical Note (constructive criticism) section after posting the article. If the section is left blank, it is intentional.

I use the term “Critical” in a broad academic sense, encompassing thorough examination, balanced evaluation, and thoughtful interpretation. It is not limited to pointing out flaws or offering negative criticism.

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