Abstract
This paper takes up a suggestion made by Floridi that the digital revolution is bringing about a profound change in our metaphysics. The paper aims to bring some older views from philosophy of mathematics to bear on this problem. The older views are concerned principally with mathematical realism—that is the claim that mathematical entities such as numbers exist. The new context for the discussion is informational realism, where the problem shifts to the question of the reality of information. Mathematical realism is perhaps a special case of informational realism. The older views concerned with mathematical realism are the various theories of World 3. The concept of World 3 was introduced by Frege, whose position was close to Plato’s original views. Popper developed the theory of World 3 in a different direction which is characterised as ‘constructive Platonism’. But how is World 3 constructed? This is explored by means of two analogies: the analogy with money, and the analogy with meaning, as explicated by the later Wittgenstein. This leads to the development of an account of informational realism as constructive Aristoteliansim. Finally, this version of informational realism is compared with the informational structural realism which Floridi develops in his 2008 and 2009 papers in Synthese. Similarities and differences between the two positions are noted.
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Notes
Many of the ideas of this lecture are also to be found in Floridi’s 2010 book. See particularly Chapter 1.
Popper and Brouwer were personal friends, and Popper told me that Brouwer had visited his (Popper’s) house near London. In chapter 3 of his (1972) which discusses his theory of the third world, Popper devotes Section 6 (pp. 128-140) to ‘Appreciation and Criticism of Brouwer’s Epistemology’. Popper describes this as a homage to Brouwer who had died not long before. Given these friendly relations, it is perhaps not surprising that Popper was influenced by Brouwer. Nevertheless, Popper’s position differs very considerably from Brouwer’s as we shall see. For more details about Brouwer’s position see Gillies (1980).
Popper himself did not like this terminology since he thought that it associated his theory with Platonism and essentialism. It should not be forgotten either that Popper regarded Plato as ‘an enemy of the open society’. Nevertheless I think that the phrase ‘constructive Platonism’ does give an accurate description of Popper’s position regarding mathematical entities.
This formulation differs to some extent from Wittgenstein’s original view. Wittgenstein in fact says (1953, p. 20): ‘ … the meaning of a word is its use in the language.’ I have, in effect, altered this to: ‘…the meaning of a word is given by its use in the language.’ The point of this change is to bring Wittgenstein’s theory more into line with the constructive Platonism now under consideration. Wittgenstein’s own formulation agrees better with the constructive Aristotelianism which will be discussed in the next section.
Marcelo Dascal kindly pointed out to me that the analogy between language and money is to be found in several 17th century thinkers, e.g. Bacon, Hobbes and Leibniz. These philosophers do not introduce the comparison to clarify the nature of abstract entities, but to make other points about language. Particularly striking is Leibniz’s comparison between words and bills of exchange, or other ‘cash-substitutes’. Cash substitutes facilitate the exchange of goods, which might otherwise be diminished by shortage of gold and silver coins. However, cash substitutes do eventually have to be converted into cash. Similarly, words facilitate thinking by allowing the mind to operate on the signs rather than always considering what these signs stand for. However, at some stage, the thinker must pass form the sign to what it denotes. For a selection of passages and a very interesting critical commentary, see Dascal (1976).
References
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Acknowledgments
The present paper was developed from a longer draft entitled: ‘Mathematical Realisms’. I circulated this among a group of my friends, namely: Carlo Cellucci, Gregory Currie, Andrew Gregory, Emily Grosholz, Christian Hennig, Ladislav Kvasz, Mary Leng, Anne Newstead, and Gianluigi Oliveri,and received many useful comments which led to improvements. On 26 November 2009, I read an extract from the longer draft entitled: ‘Are Numbers Human Constructions?’ at a seminar in the Philosophy Department of the University of Hertford. I received a number of helpful comments from the audience, particularly Brendan Larvor and Luciano Floridi. Discussions with Luciano Floridi led me to think that the problems of mathematical realism on which I had been working could be brought into relation to the more recent problem of informational realism, and this was the origin of the present paper.
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Gillies, D. Informational Realism and World 3. Know Techn Pol 23, 7–24 (2010). https://doi.org/10.1007/s12130-010-9096-6
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DOI: https://doi.org/10.1007/s12130-010-9096-6