Commensurability, incommensurability, and cumulativity in scientific knowledge

Erkenntnis 22 (1-3):51 - 77 (1985)
Abstract
Until the middle of the present century it was a commonly accepted opinion that theory change in science was the expression of cumulative progress consisting in the acquisition of new truths and the elimination of old errors. Logical empiricists developed this idea through a deductive model, saying that a theory T superseding a theory T must be able logically to explain whatever T explained and something more as well. Popper too shared this model, but stressed that T explains the old known facts in its own new way. The further pursual of this line quickly led to the thesis of the non-comparability or incommensurability of theories: if T and T are different, then the very concepts which have the same denomination in both actually have different meanings; in such a way any sentence whatever has different meanings in T and in T and cannot serve to compare them. owing to this, the deductive model was abandoned as a tool for understanding theory change and scientific progress, and other models were proposed by people such as Lakatos, Kuhn, Feyerabend, Sneed and Stegmüller. The common feature of all these new positions may be seen in the claim that no possibility exists of interpreting theory change in terms of the cumulative acquisition of truth. It seems to us that the older and the newer positions are one-sided, and, in order to eliminate their respective shortcomings, we propose to interpret theory change in a new way.The starting point consists in recognizing that every scientific discipline singles out its specific domain of objects by selecting a few specific predicates for its discourse. Some of these predicates must be operational (that is, directly bound to testing operations) and they determine the objects of the theory concerned. In the case of a transition from T to T, we must consider whether or not the operational predicates remain unchanged, in the sense of being still related to the same operations. If they do not change in their relation to operations, then T and T are comparable (and may sometimes appear as compatible, sometimes as incompatible). If the operational predicates are not all identical in T and T, the two theories show a rather high degree of incommensurability, and this happens because they do not refer to the same objects. Theory change means in this case change of objects. But now we can see that even incommensurability is compatible with progress conceived as the accumulation of truth. Indeed, T and T remain true about their respective objects (T does not disprove T), and the global amount of truth acquired is increased.
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