Empiricism, Semantics, and Ontology Rudolph Carnap [In this essay Carnap is concerned with the question of the "reality" of the sorts of what he calls "abstract entities" which are not the objects of direct observation. Examples of such "abstract objects" include the objects of mathematics, propositions in languages, classes, and relations between objects. While earlier positivists had wanted to ban "metaphysical" questions about the "reality" of things from meaningful discourse altogether, their attempt to "reduce" all knowledge to a foundation of observation statements about "sense data" in effect was committed to the metaphysical view that such "sense data" are the real things of which reality consists, a metaphysical view known as "phenomenalism. Such questions that take the linguistic framework as given are called by Carnap "internal" questions to that framework i.

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How can I get involved? To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function.

Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms. It lets you quickly and straightforwardly define languages, construct logics for those languages, and stipulate their semantics. Carnap then uses your specifications to figure out how to check proofs in a variety of formal systems using your logic, how to find the meanings of compound expressions, and a whole lot more.

Demos Here are some quick examples of what Carnap can do. You can directly manipulate the proof by typing in the proofbox, and see the effects of your changes by mousing over the line-decorations on the right hand side. Because of the number of variables, this one may take a moment to load initially. Once loaded, it should respond quickly to changes.

These use Fira Logic for nicer-looking logical symbols and use guards to help visually indicate the scope of each subproof. Carnap is intended for use by educators, students, and researchers working on logic.

Carnap makes it possible for educators to create interactive exercises and teaching materials, and for students to get quick and helpful feedback as they learn semantic and syntactic methods for determining what follows from what.

Carnap also enables researchers interested in unorthodox formal systems to rapidly prototype proof-checking and semantic tools for computer-assisted logical investigation. How can I use Carnap right now? You can use Carnap to teach your own logic class! All you need to do is create an account , and then get in touch to register as an instructor. You can either assign problems from the free textbook hosted here, or you can use your own textbook and create automatically graded problem-sets for your own preferred system.

But the ambition of the project is maximum coverage. Some tutorials for potential instructors can be found here.

Carnap is named after Rudolf Carnap, the philosopher quoted above. Carnap the philosopher famously advocated a tolerant and experimental approach to logic. Carnap the program is pluralistic by design. Inference rules are specified declaratively, making it easy to add new logics to those already provided for a given language. The algorithms for checking whether inferences are correct are applicable to a wide variety of languages, making it easy to introduce new languages.

Carnap the program is written in Haskell, a statically-typed pure functional programming language that uses a theory of logical types to ensure code correctness. How does Carnap work? There are a couple of different tricks involved. The upshot is that, using Carnap, you can define a language as the result of snapping together predefined lexical categories.

By representing a large class of languages uniformly as the result of snapping together lexical categories , we also end up being able to manipulate them uniformly. As a result, we only need to write code for these algorithms once; we can then automatically use that code with any language that can be defined in the Carnap framework.

If you have suggestions, feature requests, or bug-reports, you can create an issue on Github. An Open Tower project. Copyright G.


About Carnap

The problem of abstract entities Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists in the medieval sense. As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i. However, within certain scientific contexts it seems hardly possible to avoid them.


Empiricism , Semantics , and Ontology


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