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Empiricism, Semantics, and Ontology
Lecture Notes
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Summary
Carnap lays out the map of his paper. He wants to start by talking about what a language which refers to abstract entities (universals) looks like, and what are its implications. He then wants to argue that using such a language doesn’t mean that we’re Platonists, i.e., we believe in their objective existence.
Then he wants to talk about the role of abstract entities in semantics (meaning).
The idea is that people who want to use abstract entities, like in math, semantics, and physics, don’t need to believe in them.
Linguistic Frameworks
When someone wants to talk in a language about new kinds of entities, they have to introduce a system of ways to speak about the entity with new rules and stuff. This, Carnap says, is constructing a linguistic framework.
He says there are two kinds of existences then:
- Existence of things within the framework (internal questions)
- Existence of the entities as a whole (external questions)
Internal questions are expressed and answered by using the new form of linguistic framework constructed, where the answers may be done empirically (checking), or logically, depending on whether the framework is empirical or logical.
Carnap then goes on to address the problem of external questions.
The World of Things
Carnap brings up as an example, the world of things or the thing-world, which is just typical spatio-temporal world you and I are a part of. When answering internal questions (whether there’s a unicorn on my desk, or there’s a mug on my desk), the answers are empirical, so we test if things are true by whether they exist in the world or not. It’s done out of habit, but we can say that we can give rules for the evaluation of whether something is true or not.
If something is real, it means we’ve incorporated it into the thing-world’s system at a specific time and space in a way that fits with other things, according to the rules of the linguistic framework.
Carnap goes to the external question then, and says that in the way it is iterated, it cannot be solved, because if we question whether a system exists, then we’re asking basically if the thing exists within itself, which makes no sense.
But lets say that they’re not asking this theoretically (in whether it exists), but practically (in whether to use).
Because if someone accepts the thing-language, then they accept the world of things. However, Carnap says, this is different from believing in the reality of the thing-world, as it isn’t a theoretical question.
Thus accepting the thing-world means simply accepting a language framework.
But questioning whether to accept a language-framework is done by looking to theoretical knowledge and its usefulness. Here he says that it’s the efficinecy, fruitfulness, and simplicity which may be among the “decisive factors”.
However, these aren’t simple yes or no questions of realism, but questions of degree (how aesthetic it is, how accurate it is, etc.). So it’s more about pragmatism than it is about truth.
The System of Numbers
Carnap then looks to the example of a framework that is logical, rather than empirical.
He wants to examine the question “Are there numbers?”, and says there can be an internal formulation of it: “There are numbers.” or “There is an n, such that n is a number.” And we can move on to “Five is a number,” and so forth.
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