Saturday, February 12, 2011

Realism: Contrasting Terms

 [This continues a lexicographic/definitional thread begun here.]

Rather the way information about an analytic function in the interior of a region  may be gained from an examination of its values on the boundary,  the nature of Realism -- a multifaceted body of thought -- may be illuminated by various contrasts with what it is not.

Michael Dummett writes, in “Realism” (1963), repr. in  Truth and other enigmas (1978), p. 145:

I was told at school that the scholastic doctrine known as realism, and opposed to nominalism, had nothing whatever to do with that opinion known as realism in later philosophy, as opposed to idealism.  It was only much later that it struck me that the two disputes bore to one another an analogy which made the use of the same designation ‘realism’ for one side in each of them  more than a pure equivocation:  although the subject-matter of the two controversies differed, there was a rememblance in the form of the disputes.

(We heartily concur in this formulation.)

Dummett goes on (p. 147) -- to the admiration of this former lexicographer -- to present a list of dichotomies:

realism about material objects, oppositiion to which has traditionally taken the form of phenomenalism;
realism about the theoretical entities of science, which is opposed by scientific positivism:
realism about mathematical statements, for which I shall use the standard name ‘platonism’, employed (not altogether happily) by Bernays and Quine, opposition to which is known as ‘constructivism’;
realism about mental states … to which is opposed behaviourism.

He finishes this useful roster with “realism about the past and about the future”, but provides no antonym.  We might name it for him:  “relativistic Wal-Martia".

Further dichotomies from Dummett:

Michael Dummett, “The Structure of Appearance” (1955), repr. in Truth and other enigmas (1978), p. 29:

nominalistic [vs.] platonistic:  … those which do not, and those which do, use class-theory as part of the logical framework …

Michael Dummett, “Nominalism” (1956), repr. in Truth and other enigmas (1978), p. 42:

The platonist is he who employs in his formalism  the machinery  either of set theory  or of higher-level quantification;  the nominalist is he who dispenses with these  and uses at most  the calculus of individuals.

Michael Dummett, “Truth” (1959), repr. in Truth and other enigmas (1978), p. 18:

Intuitionists speak of mathematics in a highly anti-realist (anti-platonist) way:  for them it is we who construct mathematics; it is not already there ….

Intermediate between the anti-realist just-so-story view, and the fullbore realist account:

Fregean notion of a mathematical reality waiting to be discovered
-- id.

To all this, Dummett offers a compromise (one  to my mind, incoherent):

If we think that mathematical results are in some sense imposed on us from without, we could have instead the picture of a mathematial reality not already in existence, but as it were  coming into being as we probe.  Our investigations bring into existence  what was not there before, but what they bring into existence  is not of our own making.

Michael Dummett, “Frege’s Philosophy” (1967), repr. in Truth and other enigmas (1978), p. 88:

Frege would have to be classified as a member of the realist revolt against Hegelian idealism … but apart from his assault upon psychologism, Frege berely troubled to attack idealism at all; he simply passed it by.

Miscellaneous further dichotomies:

William James, The Principles of Psychology (1890), vol. II, p. 617:

This structure is supposed by the apriorists to be of transcendental origin, or at any rate  not to be explicable by experience;  whilst by evolutionary empiricists  it is supposed to be also due to experience, only not to the experience of the individual, but to that of his ancestors as far back as one may please to go.

Note that one can consistently hold both positions, in the following sharpened sense:  and in this sense it is in fact the position of Chomsky and his followers vis-à-vis our linguistic apparatus.   John’s linguistic (tacit) knowledge is not (fully) explicable by his own, personal experience;  one is however at liberty to suppose that his connate Language Acquistion Device may have been moulded by Natural Selection, acting upon untold generations of his ancestors.

Quine, in Hahn & Schilpp, eds., The Philosophy of W. V. Quine (1986), p. 619:
Duhem’s fictionalistic attitude toward physics  and my realistic attitude

Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. xvi:
the dichotomy between realism and constructivism:  is mathematics discovered or invented?

Susan Haack, Evidence and Inquiry (1993), p. 188:
At the strongly irrealist end, there is Rorty's proposed identification of 'true' with 'what you can defend against all comers'.

Reuben Hersh, in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. 11:

The typical working mathematician is a Platonist on weekdays  and a formalist on Sundays.

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