Abstract
The primary aim of this chapter is to present a true description of Hume’s theory of deductive sciences, viz., arithmetic and geometry, which appears scattered throughout his work; and to settle once and for all the divergent and often contradictory assertions of Hume’s critics, e.g., Kant, Baumann, Metz, Windelband, etc., on this issue. Secondarily, the aim is to show the inadequacy of Hume’s two principles, i.e., the principle of meaning and the principle of analyticity, as these principles are applied in the domain of mathematics.
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Chapter Four.
I use the term “Platonism” in the broadest sense to stand for a belief that general words, as distinct from proper names, denote non-perceptual entities, whether these entities populate the intelligible realm of Plato, or “the Universal Mind” of Leibniz, or even the “Human Mind” of Locke. In this sense Platonism also includes Conceptualism.
Hume’s Dialogues, p. 236.
Kant, The Prolegomena, loc. cit., p. 21. For the details of Kant’s argumentssee Chap. One.
H. H. Price, Thinking and Experience, 1953. “Of course images may sometimes occur in our minds when we arc thinking. But, we are told, they are merely irrelevant accompaniments of the thinking process. Indeed, they are worse than irrelevant, because they distract our attention from what we are about.…” P. 235.
S. Hampshire, “Scepticism and Meaning,” Philosophy, Vol. XXV, No. 94 (Julv. 1950).
R. W. Church, op. cit., pp. 33-36.
The relation of equality will be discussed in Section 3 (A).
John Holloway, Language and Intelligence, London, 1951, p. 8.
Locke, op. cit., Chapter 16, Book 2.
Frege, op. cit., p. 59.
Ibid., p. 58.
Ibid., p. 50.
See Chapter One.
See Passmore, op. cit., Chapter 7.
This is restatement of Wittgenstein’s dictum that: “Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question; a question only where there is an answer, and this only where something can be said. ” Tractatus.6.51.
Richard H. Popkin in his article “David Hume and the Pyrrhonian Controversy,” The Review of Metaphysics, Vol. VI, No. 1, adequately shows the relation between Hume’s scepticism and his theory of natural belief. He writes, “Pyrrhonism may be irrefutable, but nature makes us believers, and hence Pyrrhonism can be ignored. Hume once again surpasses his predecessors, ‘Philosophy would render us entirely Pyrrhonian were not nature too strong for it’ … nature does not logically refute Pyrrhonism, it only makes it unbelievable. Hume then develops his theory of natural belief showing all the beliefs of a factual, moral, metaphysical, theological and mathematical variety that nature compels us to believe.” I argue, further that Pyrrhonian arguments against possibility of establishing the validity of a demonstration is a logical blunder and hence there is no need for Hume’s theory of natural belief in order to account for our belief in the validity of a proof.
Rudolph Carnap, Logical Foundation of Probability (The University of Chicago Press, 1950), pp. 37–38.
B. Russell, My Philosophical Development, p. 234.
Ibid., p. 71.
Kant, The Prolegomena, p. 21.
Windelband, op. cit., p. 473.
Kant, Critique, p. 742.
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© 1960 Martinus Nijhoff, The Hague, Netherlands
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Zabeeh, F. (1960). The Domain of Deductive Reason. In: Hume Precursor of Modern Empiricism. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-9194-4_6
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