Empiricism Semantics and Ontology Carn

“Empiricism, Semantics and Ontology” by Rudolf Carnap
I. The Problem of Abstract Entities Empiricists attempt to limit themselves to nominalistic language, a language not containing references to abstract entities such as properties, classes, relations, numbers, propositions, etc. They treat mathematics as a mere calculus wherein no interpretation is given or can be given. However, abstract entities are impossible to avoid for some scientific contexts. The theory of meaning and truth is the problem of abstract entities in relation to semantics1. Semanticists claim that certain expressions designate certain entities, including abstract entities2. This violates the basic principles of empiricism and leads back to a metaphysical ontology3 of the platonic kind. Carnap rejects the idea that the use of such language embraces Platonic ontology, but is rather compatible with empiricism and scientific thinking.
II. Linguistic Frameworks4 Carnap believes that for someone to speak of a new kind of entities in his language, he must construct a linguistic framework, a system of new ways of speaking and is subject to new rules. To understand these entities, we must recognize the two fundamental questions concerning the reality of these entities: (1) Internal questions or the questions of existence of the new entities within the framework; and (2) External questions or the questions of existence of the system of entities as a while. Internal questions can be answered by new forms of expressions either by logical or empirical methods. External questions, on the other hand, are in need of a closer examination. The world of things is the simplest kind of entities we deal with everyday language and upon our acceptance of the thing language with its framework for things, we can raise internal questions like “Is there a white piece of paper on my desk?”, “Are unicorns real or imaginary?” and these can be answered by empirical investigation. The results of this investigation can be confirmed or disconfirmed based on explicit rules for the evaluation, which is the main concern of epistemology. The rules of the framework claim that in order for something to be considered real, it must fit into a system at a particular space-time position along with other things considered as real. The external question of the reality of the thing world is not asked by scientists but by philosophers and is given affirmative answers by realists, and negative answers from subjective idealists. This question is never resolved because it is wrongly framed. To be real in the scientific context means to be an element of the system, hence, this concept cannot be meaningfully applied to the system. Those who question the reality of the thing world are not expecting of a theoretical question, rather, a practical question which would affect the structure of our language; hence, we must decide whether or not to adapt the forms of expression in the framework. We have accepted the thing language since our earlier years and now we are given the choice whether or not to continue using the thing language or to restrict ourselves to sense-date, to construct an alternative language with new structure and rules, or to refrain from speaking at all. However, Carnap believes that none of the above-mentioned choices is practical. So, he explained that the acceptance of the thing language does not imply the acceptance of the existence of the thing world, but the acceptance of a certain form of language, accepting rules in order to form, test, or reject statements, and the idea of the reality of the thing world cannot be among these statements because it cannot be formulated in the thing language or in any other theoretical language. Questions regarding the efficiency, fruitfulness and simplicity of the use of the thing language are not yes-no questions but rather questions of degree. But it is wrong to say that “The fact of the efficiency of the thing language is confirming evidence for the reality of the thing world,” rather, “This fact makes it advisable to accept the thing language.” Carnap used the example of the system of numbers as an example of a system which is of a logical rather than a factual nature, based on the rules of the new expressions: (1) numerals like “five” and sentence forms like “there are five books on the table” (2) the general term “number” for the new entities, and sentence forms like “five is a number” (3) expressions of properties of numbers (odd, prime), relations (greater than), and functions (plus), and sentence forms like “two plus three is five.” (4) numerical variables (m,n,etc) and quantifiers for universal sentences (for every n,….) and existential sentences (there is an n such that…) with the customary deductive rules Empirical investigation is impossible to answer the internal question, “Is there a prime number greater than a hundred?”, rather it can be answered through logical analysis. He also introduced the system of propositions wherein any declarative sentence can be substituted by a variable. Every sentence that comes in the form “…is a proposition” is considered analytic. This framework included three constructs: (1) “For every p, either p or not –p” (2) “There is p such that p is not necessary and not –p is not necessary.” (3) “There is p such that p is a proposition.” (1) and (2) are both internal assertions of existence while (3) is an implication that there are propositions. Lastly, in the spatio-temporal coordinate system for physics, the new entities are the space-time points. Each point is an ordered quadruple of four real numbers (3 spatial and 1 temporal coordinate). It is not forced on us but is suggested by common observation. The physical state of these space-time points is described through qualitative predicates or through ascribing numbers such as mass, temperature, etc. Moving on to this physical coordinate system requires a decision on how to use language. Carnap argues that the introduction of such forms into our language is a matter of degree, and that the formulation in the form “real or not” will be inadequate. Many philosophers argue that the affirmation of the reality of the entity of the language shall come prior to the introduction of new language forms, and Carnap strongly disagrees. He claims that a new way of speaking needs not be justified because in the first place, it does not imply any assertion of reality, but only acceptance of a new framework.
III. What Does Acceptance of a Kind of Entities Mean? The acceptance of a new kind of entities is represented in the language by the introduction of a framework of new forms of expressions to be used according to a new set of rules. The two essential steps into the introduction of the framework are: (1) the introduction of a general term, a predicate of higher level, for the new kind of entities, permitting us to say of any particular entity that it belongs to this kind5; and (2) the introduction of variables of the new type. After the formulation of the new forms of language, they can now create internal questions that may either be empirical or logical, and be addressed by true answers that are either factually true or analytic. Carnap debunks the idea that the acceptance of a new framework is an assertion of the reality of the entities. He argues that the question whether or not to accept the new entities and the new linguistic form is a practical question and not a theoretical question. It cannot be judged as true or false because it is not an assertion, rather, it can be judged as being more or less expedient, fruitful and conducive.

IV. Abstract Entities in Semantics In semantical meaning analysis, certain expressions are often said to designate (or name or denote or signify) certain extra-linguistic entities. Ex. “The word ‘red’ designates a property of things.” “The word ‘five’ designates a number.” Empiricists admit that these are meaningful expressions but reject the belief as they see these as implicitly presupposed by those semantical statements. This belief is criticized as hypostatization, or treating as names expressions which are not names. Carnap used the example of “Fido”, his dog, as a name that designates his dog Fido, while red and five are not names and are not supposed to designate anything.
To deal with this criticism, Carnap clarifies abstract entities as designata: (a) "'Five' designates a number." This presupposes that our language L contains the forms of expressions which we have called the framework of numbers, in particular, numerical variables and the general term "number". If L contains these forms, the following is an analytic statement in L.
(b) "Five is a number." To make the statement (a) possible, L must contain an expression like "designates" or "is a name of" for the semantical relation of designation. If suitable rules for this term are laid down, the following is likewise analytic:
(c) "'Five' designates five."

Since (a) follows from (c) and (b), (a) is likewise analytic. You must accept these as true statements if you accept the framework of numbers.
Carnap acknowledges the need for theoretical justification for internal assertions but argues that it is wrong to demand for such when it comes to acceptance of system of entities. He cites Ernest Nagel who asked for "evidence relevant for affirming with warrant that there are such entities as infinitesimals or propositions." He required the evidence to be logical and dialectical. And so Carnap provides an example of this problem of proof:
“Here are three books.” The framework of the sentence allows us to communicate but the question on the ontological reality of the system of numbers continues. One philosopher believes that numbers are real entities so there is no problem in using the numerical framework for semantical statements. A nominalistic opponent, on the other hand, says there are no numbers. For Carnap, numbers may still be used as meaningful expressions but they are not names and there are no entities designated by them. The term numbers and numerical variables must only be used as abbreviating devices: i.e. to translate them into the nominalistic thing language. He believes that there is no possible evidence relevant for both philosophers.
V. Conclusion Carnap’s stand on using semantical methods depended not on the ontological question of existence of abstract entities but on the question whether or not the rise of abstract linguistic forms is expedient and fruitful for semantical analyses6. This is no yes-or-no question. It dealt with a matter of degree, by their efficiency as instruments, by the ". . ratio of the results achieved to the amount and complexity of the efforts required." He challenges the nominalists to offer better arguments than merely appealing to ontological insight; probably a semantical method without any references at all to abstract entities and by simpler means, achieves the same results as other methods. Carnap pointed out that dogmatic prohibitions are both futile and harmful that looking back to history, traces of slow development rooted to religious, metaphysical, mythological, and other irrational sources. And so by granting freedom to use any form of expression useful to them, those useless forms will sooner or later be eliminated. Carnap ended with a reminder, “Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms.”