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Laudan's problem solving model.

A historical example is considered which conflicts with Laudan's Problem Solving Model [1981]. In the period 1840--85 chemists preferred a theory with 3 major conceptual problems (the Liebig Theory of Acids) to Lavoisier's which had only one major conceptual problem (why are the halogen hydrides acids?). The overall conceptual merits of Lavoistier's scheme have been revived in the modern Lux-Flood classification of Acids.

Larry Laudan [1977], [1981] proposed a problem solving model of scientific rationality which not only applied to global theories but, if one takes the final paragraph of his [1977] seriously, also applies to sub theories, auxiliary hypotheses and sub auxiliary hypotheses all the way down the line.

According to Laudan [1981] science progresses just in case successor theories solve more problems than their predecessors. Laudan claims that theory evaluation must be a comparative affair since he feels that Popper's criteria of verisimilitude and cumulative retention are inadequate. He advocates a 'cost benefit analysis' approach in which credit is assigned to a theory for the number of problems it has successfully solved, modified by a weighting factor for the relative importance of each problem. Credit = [sigma] w, p,..... [w.sub.n] [p.sub.n] where w = weighting of problem importance p = problem Laudan also allows for a kind of 'infant industry' philosophy in which he allows that it is rational to develop a promising new theory which solves a major conceptual problem not solved by its predecessor although the overall problem solving ability of the new theory is much less. However, he makes it clear that such a theory is definitely 'on probation' and there is no question that the predecessor theory is to be abandoned because of one and only one flaw.

An instructive example, apparently supporting Laudan's problem solving model, from the history of chemistry is the transfer of allegiance of scientists from the Liebig Hydrogen Theory of Acids to the Arrhenius Theory of Acids after it was first proposed in 1885.

Leibig's Theory, first enunciated in 1839, proposed that acids were hydrogen salts i.e., the molecule contained 'active' hydrogen replaceable by a metal atom to form a salt. For example, the formula for acetic acid should not be written [C.sub.2][H.sub.4][O.sub.2] but [HC.sub.2][H.sub.3][O.sub.2] to emphasize the role of the 'active' hydrogen in forming the salt sodium acetate [NaC.sub.2][H.sub.3][O.sub.2]. However, this theory contained several conceptual problems.

(1) Why did concentrated acids behave in a different way to the diluted varieties?

(2) Why did increased oxygen content in the acid seemingly correlate with increased acidity?

(3) Why wee some dihydric and trihydric acids weaker than some monohydric acids ([H.sub.3][PO.sub.4] is weaker than [HCIO.sub.4]).

These problems were overcome by the bold proposal by Arrhenius in 1885 that acids dissociated spontaneously into ions on dissolution in water without the need for the input of electrical energy viz. HCl[O.sub.4][equilibrium][H.sup.+] + Cl[[O.sub.4].sup.-] [H.sub.3]P[O.sub.4][equilibrium][H.sup.+] + [H.sub.2]P[[O.sub.4].sup.-] [equilibrium][H.sup.+] + HP[[O.sub.4].sup.=][equilibrium][H.sub.+] + P[[O.sub.4].sup.[equivalent]] The role of the oxygen was to stabilize the negative counter ion forcing the equilibrium to the right, the acidic properties of dilute acids was a function of the concentration of [H.sup.+] ions at equilibrium and the 'surprising' weakness of trihydric acids due to the fact that it became increasingly less energetically favourable for a negative ion such as [H.sub.2]P[[O.sub.4].sup.-] to release [H.sup.+] than the neutral molecule [H.sub.3]P[O.sub.4].

Without the complication of any new existence claims Arrhenius' theory seems preferable on a problem solving calculus and scientists who accepted it were rational by Laudan's standards. But wait: the 3 conceptual problems outlined above were also solved by the Lavoisier Theory of Acids as developed by Fourcroy in [1788], (Akeroyd [1990]).

(1) The metals cannot combine with the acids but after they have been oxided or combined with oxigene (sic).

(4) In every metallic solution by an acid the metal, in order to become oxided, decomposes either the acid itself or the water of solution, or obtains from the atmosphere the requisite quantity of oxigene (sic). In the second case hydrogenous gas, in a state of greater or lesser impurity, is disengaged and the acid remains entire without decomposition. It is obvious when one reads the whole of Fourcroy's position paper that he has extended Lavoisier's original empirical generalisation 'All acids appear to contain oxygen as an essential consitutuent' to a conceptual generalisation essentially a forerunner of the Lux--Flood Definition of Acids (first proposed in 1948) and still used today in non aqueous molten systems (see Dearnaley et al. [1985]). In this definition an acid is regarded as an oxide acceptor and a base as an oxide donor.(1)

However, in the period 1840--85 most chemists preferred the Liebig Hydrogen Theory of Acids (warts and all) obviously using other criteria to the problem solving calculus. It would appear that they used Popperian style deductive logic in conjunction with the modus tollens. If the class of strong hydrohalic acids contained no oxygen then it could not be the case that oxygen was the essential component of an acid, the observation of one black swan was decisive in this particular instance.

The formation of an acid solution when hydrogen chloride gas dissolves in water can be accommodated by stating that HCI is a proton donor (Bronsted definition) HCl + [H.sub.2]O[right arrow]C[l.sup.-] + [H.sub.3][O.sup.+] or an oxide acceptor (Lux--Flood) HCl + [H.sub.2]O[right arrown][H.sub.3][O.sup.+] + C[l.sub.-] The chemical reactions of this acid solution with solid oxides, carbonates and solutions of hydroxide ions can be regarded as proton transfer from acid to base (Bronsted) or oxide donation from base to acid (Lux--Flood) 2[H.sub.3][O.sup.+] + [O.sup.=] [right arrow] 3[H.sub.2]O 2[H.sub.3][O.sup.+] + C[[O.sub.3].sup.=] [right arrow] 3[H.sub.2]O + C[O.sub.2] [H.sub.3][O.sup.+] + O[H.sup.-] [right arrow] 2[H.sub.2]O

(1)Cotton, Wilkinson and Gaus state in an undergraduate textbook: 'The Lux--Flood concept of acids and bases is veryuseful in dealing with high temperature, anhydrous systems such as those encountered in the oxide chemistries of ceramics and metallurgy. Furthermore the Lux--Flood definition has a direct relation to the aqueous chemistry of acids and bases because the bases are oxides (basic anhydrides) that react with water as in Eq. 7--8.16: N[a.sub.2]O + [H.sub.2]O[right arrow]2N[a.sup.+] + 2O[H.sup.-] (7--8.16) and the acids are oxides (acidic anhydrides) that react with water as in Eq. 7--8.17: [P.sub.2][O.sub.5] + 3[H.sub.2]O[right arrow]2[H.sub.3]P[O.sub.4] (7--8.17) Lavoisier wrote in 1789: 'From these phenomena it appears that oxygen is the bond of union between metals and acids; and from this we are led to suppose that oxygen is contained in all substances which have a strong affinity with acids: Hence it is very probably the four eminently salifiable earths contain oxygen and their capability of uniting with acids is produced by the intermediation of that element'.


AKEROYD, F. M. [1990]: 'The Challenge to Lakatos Restated', British Journal for the Philosophy of Science, 41, 437--9.

COTTON, F. A., WILKINSON, G. and GAUS, P. L. [1987]: 'Basic Inorganic Chemistry', 2nd edition, p. 214. New York: J. Wiley & Sons.

DEARNALEY, R. I., KERRIDGE, D. H. and ROGERS, D. J. [1985]: 'Molten Lithium Sulfate--Sodium Sulfate--Potassium Sulfate Eutectic: Lux--Flood Acid-Base Reactions of Transition--Metal Sulfates and Oxides', Inorganic Chemistry, 24, pp. 4254--8.

FLOOD, H. and FORLAND, T. [1947]: 'Acidic and Basic Properties of Oxides', Acta Chemica Scandinavica, 1, pp. 592--604.

FOURCROY, A. [1789]: 'Concerning the Dissolution of Metals', in Kirwan, R. [1789]: 'An Essay on Phlogiston and the Constitution of Acids', facsimile edition, London: F. Cass [1968], p. 233.

LAVOISIER, A. [1788]: 'Elements of Chemistry', translated R. Kerr, Fascimile edition [1965], p. 164. London: Dover Publications.

LAUDAN, L. [1977]: 'Progress and its problems'. Berkley, CA: University of California Press, p. 225.

LAUDAN, L. [1981]: 'A Problem-Solving Approach to Scientific Progress' in 'Scientific Revolutions', ed. I. Hacking. Oxford: Oxford University Press. pp. 144--55.

LEICESTER, H. M. [1971]: 'The Historical Background to Chemistry', London: Dover Publications. pp. 208--9.

LUX, H. [1939]: '"Sauren" und "Basen" im Schmelzfluss', Zietschrift fur Elektrochemie, 45, pp. 303--9.
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Title Annotation:Discussion; Larry Laudan
Author:Akeroyd, J. Michael
Publication:The British Journal for the Philosophy of Science
Date:Dec 1, 1993
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