The Statistical Philosophy of W.F.R. Weldon


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The argument between the biometrical school and the Mendelians is one of the most often-cited debates on the structure of evolutionary theory in the years immediately following Darwin's death in 1882. The disagreement between the two parties manifested itself in many forms, and cannot strictly be said even to be about Mendelian genetics – thebattle lines had been clearly drawn as early as 1893, seven years before the “rediscovery” of Mendel's work. The central argument is frequently described as a dispute over the proper interpretation of evolutionary theory – particularly as a debate between saltationists and gradualists. Another view (that of the social constructivists) sees the key issue to be Karl Pearson and Francis Galton’s focus on eugenics. However, a string of acrimonious correspondence published in Nature in 1895 and 1896, I argue, doesn't fit either of these simple molds. In this paper, I argue that we can only make sense of this correspondence if we see the Batesonians (the best name, I think, for the proto-Mendelians) as reacting against the philosophical content of the biometricians' work – particularly, the influence of Machian phenomenalism on Karl Pearson, and W.F.R. Weldon's views on causation. It is this philosophical context, rather than either the rate of evolutionary change or the impact of eugenics, that enables us best to understand the way the parties to the debate understood what was at stake.

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The Statistical Philosophy of W.F.R. Weldon

  1. 1. University of Notre DameProgram in the History and Philosophy of ScienceDepartment of PhilosophyThe Statistical Philosophyof W.F.R. WeldonISHPSSB ’09Charles
  2. 2. Weldon on Statistical MethodMen measure a certain thing, and find that up to a certainpoint their measurements agree with each other, and theirexperience is uniform; but beyond that point, theirexperience is contradictory. Having made this contradictoryrecord with as much care as they can, they substitute for itone constant value of the thing measured. But the questionalways arises, how far this proceeding is justified, – how farthe variability of the actual experience depends uponimperfect observation, and how far it is a true record ofdifferences in the thing measured.— Weldon (1906), p. 88
  3. 3. Weldon on Statistical MethodIf we want to make a statement about the stature ofEnglishmen, we must find a way of describing our wholeexperience; we must find some simple way of describingour whole experience, so that we can easily remember andexplain to others how many men of any given height wefind among a thousand Englishmen. We must give up theattempt to replace all our experiences by a simple averagevalue and try to describe the whole series of results ourobservation has yielded.— Weldon (1906), p. 94
  4. 4. Weldon on Statistical MethodAll experience, which we are obliged to deal withstatistically, is experience of results which depend upon agreat number of complicated conditions, so many and sodifficult to observe that we cannot tell in any given casewhat their effect will be.— Weldon (1906), p. 97
  5. 5. Conclusions• The standard historical story:• Mach’s positivism → Pearson• Pearson’s positivism (+ biology) → Weldon• Pearson + Weldon → (positivist) biometry
  6. 6. Conclusions• The standard historical story:• Mach’s positivism → Pearson• Pearson’s positivism (+ biology) → Weldon• Pearson + Weldon → (positivist) biometry• But Weldon’s philosophy of science is far from being acarbon copy of Pearson’s – perhaps the better story is:• Mach’s positivism → Pearson 〚→ statistics 〛• Hume / Scottish empiricism (?) → Weldon’s statisticalphilosophy 〚→ statistics 〛• Pearson + Weldon → (statistical) biometry
  7. 7. Questions?