Abstract
The establishment of the first scientific theories, necessarily involving the clarification of the words borrowed from ordinary language and the development of the criteria necessary for the specification of the objects of sciences, inevitably led to the study of the logical method known as definition (ὁρıσμόϛ, definitio).1
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Plato, Theaetetus, Moscow-Leningrad 1936.
Aristotle, Topics.
Aristotle, Analytics, Moscow 1952.
Robinson, R., Definition, Oxford 1950.
Dubinslaw, W., Die Definition, Leipzig 1931.
Uspenskij, V. A., Lekcii o vycislimyx funkcijax [Lessons on Computable Functions], Moscow 1960.
Aristotel’, O castjax zivotnyx [De partibus animalium], Moscow 1947.
Lokk, D., Opyt o celoveceskom razume [Essay…], Moscow 1960.
Meyer, H., ‘On Definitions in Symbolic Logic’, Synthese5, 5–6 (1946), 338.
Whitehead and RUSSELL, Principia Mathematica, Cambridge 1925.
Vitgenstejn, L., Logiko-filosofskij traktat [Tractatus], Moscow 1958.
Carnap, R., ‘Foundations of Logic and Mathematics’, in: International Encyclopedia of Unified Science, Chicago 1939.
Definition’, in: Encyclopedia Britannica, 1957.
Rassel, B., Celoveceskoe poznanie [Human Knowledge], Moscow 1957.
Bridgman, P. W., The Logic of Modern Physics, New York 1954.
Pselenskij, T., O tak nazyvaemyx operacionnyx opredelenijax [On the so-called Operational Definitions].
Frank, P., Filosofija nauki [Philosophy of Science], Moscow 1960.
Hao Wang, ‘Ordinal Numbers and Predicative Set-Theory’, Zeitschrift f. mathematische Logik u. Grundlagen der Mathematik, 5, 3/4.
Materna, R., Zu einigen Fragen der modernen Definitionslehre, Praha 1959.
Curry, H., FEYS, R., and CRAIG, W., Combinatory Logic, Amsterdam 1959.
Klini, S. K., Vvedenie v metamatematiku [Introduction to Metamathematics], Moscow 1957.
Lenin, V. I., Imperializm, kak vyssaja stadija kapitalizma [Imperialism as the Highest Stage of Capitalism], Soc, t. 22.
Engel’s, F., Anti-Djuring, Moscow 1945.
Engel’s, F., Dialektika prirody [Dialectic of Nature], Moscow 1941.
Gorskij, D. P., Voprosy abstrakcii i obrazovanie ponjatij [Questions of Abstraction and the Formation of Concepts], Moscow 1961.
Lenin o profsojuzax [Lenin on Trade-Unions], Moscow 1957.
References
ὁρıσμόϛ comes from the Greek word ‘horos’ which means ‘limiting post’: such posts serve to delimit one field from another. Definitio comes from the Latin finis which also means the limit, or end of something.
Euclid’s works are symptomatic in this regard: the geometrical works contain axioms and postulates in addition to definitions; the arithmetical ones contain only definitions.
For an interesting discussion on how various philosophers and logicians view the process of definition, see [4].
This sometimes takes the form: does one define the meaning of the term, or the thing designated by the term, or the concept expressed by the term? The last was particularly held by German conceptualism from Kant to Rickert. Most textbooks on logic reflect this view and it is strengthened by the generally accepted terminology, as when one says the definition of the concept. However, some conceptualists tend to take definitions as nominal while others take them as real (especially the materialist logicians). This difference is expressed in the fact that the first stress the ‘creative’ (arbitrary), conventional character of definitions (concepts are the result of free creative activity), while the second stress the determination of every definition by the defined object. All these views are summed up in the alternative: nominal or real definitions, which we will take up in the present work.
Even before Socrates, who only used the process of definition for the explanation of ethical principles based on the development of the evaluation of ethical facts and examples, Democritus (according to Aristotle) tried to explain the essence of the process of definition as the explanation of the essence of being [7; 1, 642a 25–28].
Church offers a similar definition in [13].
We should note that not all writers on the subject consider such ‘pure abbreviations’ as definitions. Reichenbach is one of these. But, Church regards such abbreviations as definitions.
Russell is right when he says that in such cases we are using narrative statements in their elliptical form [14; Part II, Ch. II].
In the analysis of these definitions we will use materials from [15], [16], [17; 188–212].
In formal-logical textbooks this requirement is usually formulated as follows in relation to the definition through genus and specific difference: the extension of the concept defined has to be equal to that of the concept defining so that they are inter-changeable.
In any case, if one agrees to consider ‘definitions through abstraction’ as definitions, we can see no reason for refusing to consider these operational statements as definitions.
Though the designans (the sign) and the designatum (the object) are both material, sense-perceptible objects, they cannot be identified. These problems are analyzed, for example, by Russell in connection with the establishment of the so-called ramified theory of types.
This expression is assumed (sensefully) defined for any values of the variables x1,…, x j .
All these types of definition are considered in Materna’s [19]. We should note that Materna does not analyse the definition from the point of view of the rules of introduction and exclusion of newly introduced terms.
On this point, see a similar analysis of ‘paradoxical combinatories’ in [20] by Church and Feys.
These and the others should not be confused with proofs through induction.
We are here talking about sets and not about domains of individuals since we have in mind non-fundamental inductive definitions.
We have specially taken up this question in [25; Ch. II].
On this point, see Section 2, Point 4 of this article.
There are other sources of terminology, which we will not take up here.
Editor information
Rights and permissions
Copyright information
© 1970 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Gorskij, D.P. (1970). On the Types of Definition and Their Importance for Science. In: Tavanec, P.V. (eds) Problems of the Logic of Scientific Knowledge. Synthese Library, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3393-0_8
Download citation
DOI: https://doi.org/10.1007/978-94-010-3393-0_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3395-4
Online ISBN: 978-94-010-3393-0
eBook Packages: Springer Book Archive