2+2=5 STSの場合

以前も触れたが、STS学者Barry BarnesとSTS学者David Bloorと歴史学者John Henryは、「創造論は疑似科学の汚名を着せられている」と言う。

In some way Gauquelin is fortunate in merely being ignored; many practitioners of 'genuine science' fare no better. Other producers of 'suspect' work which nonetheless has prima facie claims to be scientific encounter active hostility. Parapsychology and creationism, for example, continue to be attacked and stigmatized as pseudo-scientific and the 'pretensions' of their practitioners are often ridiculed. Nor is the way that such fields are discriminated from 'genuinely scientific' enterprises invariably fair and even-handed. Often historically specific criteria of good science are selectively applied, and 'pseudo-sciences' are condemned as such on the basis of tests which most currently accepted genuine sciences would surely fail (Collins and Pinch 1982).

ある意味、Gauquelinは無視されただけで幸運だった。多くの「本物の科学」の実践者たちは、それより良くない。「疑わしい」成果を出した実践者たちは、一応は科学的主張を持っているのだが、活発な敵意に遭遇する。たとえば、超心理学と創造論は、常に攻撃され、疑似科学の汚名を着せられ、実践者の自負は嘲笑され続ける。またそのような分野は、常に公平で公正な「本物の科学」界から差別されている。歴史的には、良い科学の規準は選択的に適用されていて、現在受け入れられている本物の科学でも確実に失敗するテストに基づいて、疑似科学だと非難されている。

[Barry Barnes, David Bloor, and John Henry: "Scientific Knowledge:A Sociological Analysis", 1996, p.141]

いかにも創造論者の主張みたいだが、STS学者の主張である。

彼らの主張はこれに留まらない。

ドストエフスキーやユーゴーやツルゲーネフやトルストイが不条理の象徴として使い、旧ソビエト連邦の5カ年計画のスローガンとなり、「ウィンストン・スミスが、国家が事実として主張する可能性を考え」ようとした2+2=5を掲げる。

If this supports the view that we could have a convention in which 2 + 2 = 5, then it will be asked: why don't we have it? Why do we say 2 + 2 = 4 rather than 2 + 2 = 5, or all the other things we apparently could say? The objection lurking behind this query is that our current mathematical conventions might be more than 'just' conventions. They might have been selected or reinforced because they 'correspond' to some truth, or because they are informed by some uniquely rational virtue that singles them out. 

The naturalistic response must be to take the question seriously, but to insist that if it has an answer it will not be in terms of our practices 'corresponding' to some mysterious mathematical reality. It will be for some naturalistically explicable psychological and social reasons. Consider, for example, why we might have a preference for what Lakatos called ' weightless' addition (where 2 + 2 = 4), rather than one of the indefinitely large number of alternatives. A sociological answer might appeal to principles of the following kind: to establish a convention for addition means solving a coordination problem, that is, it means getting everybody to adopt the same procedure. Coordination problems are easier to solve if they have a 'salient solution', one that is automatically visible to everyone and where everyone routinely assumes that it is visible to everyone else. Salient solutions are often extreme solutions, ones which lie prominently at the beginning or end of the spectrum of alternatives. Weightless addition may be such an extreme and prominent solution. There are therefore pragmatic reasons connected with the organization of collective action that would favour saying 2 + 2 = 4, rather than 2 + 2 = 5 or 6 or 7 or .... As a convention it is probably easier to organize than the others, and therefore more likely to arise histrically.

[Barry Barnes, David Bloor, and John Henry: "Scientific Knowledge:A Sociological Analysis", 1996, P. 185]

こういった主張は、米国の数学教育を蝕むという実害をもたらしたようだ。