Abstraction

Abstracting a concept from a base - some data or a more concrete concept - means identifying those features that are constitutive of the concept, i.e. that are taken as crucial in subsuming or not an object under the concept, while at the same time ignoring (leaving unspecified) all those properties which the objects covered possess in addition but which are immaterial to the concept in question. For instance, we abstract the concept of a table from our experience with a set of tables. This concept does not comprise the color of the table(s). This is so despite the fact that all real tables have colors. The concept does not deny this, it just leaves it open.

Abstraction of a relational notion involves leaving its arguments open. Thus, the notion of a certain property like validity is abstracted from propositions whose predicate ascribes this property to their subject – in this case, ‘X is valid’ –, by leaving X open. Likewise, the notion of a certain act – e.g. ‘definition’ – is abstracted from propositions of the form ‘X defines Y’, where X and Y are left open.

Abstraction is essentially a step in an inductive procedure, although it may be guided (deductively) by more general principles. The more abstract a concept is, the farther it is removed from observable phenomena. It is then all the more necessary to operationalize it; otherwise the theory using it will not be falsifiable.

Idealization

A construct of thinking is an idealization of some concept iff it changes or omits any of the features constituting that concept in order to simplify it. In an idealization, we assume a state of affairs that does not correspond to known reality. We do so in a methodological situation where our subject matter is so hopelessly complex that we are incapable of proposing a theory all of whose concepts are interrelated in such a way as to cover appropriately the interactions of the objects meant by them. In such a situation, we limit our epistemic interest by singling out a concept and disregarding part of its complexity. We might, e.g. construct a concept of a colorless table, i.e. a table that does not reflect light. That would be an idealization that is incompatible with our experience of tables, which teaches us that all tables have a color. (See elsewhere for the concept of language as an example.) Moreover, there is by definition no methodological procedure that would allow us to pass from the idealized concept to the basic concept (from a colorless table to a real table). If there were, the idealization would be unnecessary.

Examples of idealizations made in the history of science include the free fall, i.e. a fall which occurs in a complete vacuum, and the competence of the ideal native speaker, i.e. an infallible human being.

An idealization cannot be arrived at inductively, it can only be deduced from axioms or (failing that) be stipulated.

Operationalization

The definition of a concept of an empirical science comprises its operationalization. The operationalization of a concept – and mediately, of a theorem or hypothesis using it – consists of a set of criteria and a set of methodological operations specifying the application of such criteria to some observable phenomenon. It allows one to ascertain whether or not the phenomenon falls under the concept. This typically involves the specification of a test that some phenomenon must pass in order to be subsumed under the concept or, on the contrary, the specification of certain phenomena that would, if they occurred, falsify a certain theorem.

A theory is an empirical theory, i.e. a theory of an object area existing independently of it, only if its concepts and theorems can be operationalized. Thus, operationalization of the concepts and theorems of a theory is an essential step in rendering it falsifiable and, thus, empirical. For examples, see the operationalization of the concepts of presupposition and of terminative aktionsart.

Since an idealized theoretical construct is one that comprises features which contradict known reality, it is by definition neither falsifiable nor operationalizable. This means that one admits idealizations in the construction of a theory at the cost of immunizing it against falsification, i.e. of depriving it of the status of an empirical theory. The question of whether such a theory should be pursued in a science is then, ultimately, a question of the epistemic interest of the people responsible for that scientific activity.