Abstract
We must now look more closely at the concept as a mental entity. Remembering that one cannot imagine a man who is neither young nor old, tall nor short, that is, a man in general; likewise, that every triangle must be imagined either acute, obtuse or right-angled, so that there is no triangle in general: we might easily conclude that there are no such mental constructs as concepts at all, nor abstract ideas, a denial that Berkeley had defended with special vigour. However, we might just as easily be led to the view of the ‘nominalist’ Roscelin that general concepts or universals do not exist as things but are mere ‘flatus vocis’, while his ‘realist’ opponents regarded them as grounded in things. That general concepts are not, as a respected mathematician asserted quite recently, mere words, clearly emerges from the fact that very abstract propositions are understood and correctly applied in concrete instances, witness the countless applications of the proposition “energy remain constant”. It would however be idle to attempt to find a clear, momentary conscious idea which would exactly cover the sense of the sentence as it is spoken or heard. The difficulty disappears if we recognize that concepts are not momentary entities, like a simple concrete symbolic idea: every concept has its sometimes long and eventful formative history, and its content cannot be explicitly expounded by a transient thought.1
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Notes
A psychological theory of concepts is attempted in my A 4, pp. 249–255; P 3, pp. 277–280; W 2, pp. 415–422. Cf. further H. Rickert, ‘Zur Theorie der naturwissenschaftlichen Begriffsbildung’, Viertelj. f. wiss. Philosoph., Vol. 18, 1894 p. 277
H. Gomperz, Zur Psychologie d. logisch. Grundtatsachen, Vienna 1897
Th. Ribot, L’évolution des Idées générales, Paris 1897
M. Keibel, ‘Die Abbildtheorie u. ihr Recht in d. Wissenschaftslehre’, Zeitschr. f. immanente Philos., Vol. 3 1898.
Finally I wish to refer to A. Stöhr, Leitfaden der Logik in psychologisierender Darstellung, Vienna 1905, which appeared at the same time as the first edition of the present work. Its very first pages contain an original elucidation of the theory of concepts from the standpoint of neuron theory.
Cf. Ch. VII, end of sn. 5.
Cf. W, p. 146.
Cf. A, p. 250.
Cf. ibid., p. 253.
I myself have had occasion to convince myself how futile it is to urge people towards abstraction. Children will readily grasp and distinguish small sets or groups of objects and quickly give the correct answer to the question ‘how many nuts are three nuts and two nuts?’ but be embarrassed by the question ‘how much is two and three?’. A few days later the abstract formula will come of its own.
When my boy was between four and five I gave him a small box of wooden models of geometrical bodies which I named without of course defining them. His visual imagination was greatly enriched by this and his phantasy strengthened so much that he could for example count the corners, edges and faces of a cube or tetrahedron without seeing the model. He even used the new objects and their names to describe his own small observations. Thus he called a sausage a curved cylinder. Nevertheless, he had as yet no geometrical concepts. The definition of a cylinder would have to be quite different from the usual one if the shape of a sausage is to count as a special case of it.
Cf. the statistical data collected in Ribot, l.c., pp. 131–145. As regards the ‘type auditif’ p. 139 he advances the attractive hypothesis that in the age of mediaeval oral instruction and the then current oral disputations this type was perhaps preponderant and that the origin of the expression ‘flatus vocis’ may be due to this circumstance.
Let me again refer to the book of Stöhr (note 1 above). Note what he calls ‘Begriffszentrum’.
One might thus well say that simple sensations are abstractions, but one must not therefore assert that they are based on no actual process. Consider pressure and acceleration. Cf. P 3 & 4, p. 122.
Cf. Ch. VII of this volume.
A 4, p. 253.
Ibid. p. 248 and Ch. VII sn. 3 of this volume.
Apelt, Die Theorie der Induktion, Leipzig 1854, p. 59.
Ibid. p. 60.
Whewell, Geschichte der induktiven Wissenschaften, German translation by J. J. v. Littrow, Stuttgart 1840, II, p. 31.
Apelt, l.c., pp. 60, 61.
Whewell, The Philosophy of the inductive sciences, London 1847, I, p. 216.
M 5, 1904, pp. 140–143.
Whewell, Geschichte II, p. 31; Wohlwill, Galilei und sein Kampf für die Kopernikanische Lehre, Hamburg 1909.
Apelt, l.c., pp. 61, 62.
Ibid., pp. 62, 63.
Volkmann, Einführung i. d. Studium d. theoretischen Physik, Leipzig 1900, p. 28.
In Erhaltung der Arbeit 1872, M 1883 and W 1896 I have explained these views in detail as regards physics.
J. B. Stallo, The Concepts and Theories of modern Physics, 1862, German ed. Entitled Die Begriffe und Theorien der modernen Physik, by H. Kleinpeter with a preface by E. Mach, Leipzig 1901. Cf. especially pp. 126–212.
J. F. Fries, Die mathematische Naturphilosophie, Heidelberg 1822, p. 446.
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© 1976 D. Reidel Publishing Company, Dordrecht, Holland
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Mach, E., Hiebert, E.N. (1976). The Concept. In: Knowledge and Error. Vienna Circle Collection, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1428-1_8
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