Ambiguity

In reconstructing arguments, we have to eliminate any ambiguities in the original statement of the argument. If the original statement contains an ambiguous sentence, we have to decide which of the possible interpretations was most likely intended by the arguer, and, in our reconstruction of the argument, rewrite the sentence, choosing a form of words which conveys the intended meaning unambiguously.

Let us take an example. Suppose that Jane, a Londoner, decides to invest some money in the share market. She decides to look for an investment adviser, and finds an advertisement which runs as follows:

Sharemasters: London's leading personal investment advice service\

Suppose that this expresses a true proposition, and Jane accepts that what it says is true; she accepts that Sharemasters is London's leading personal investment service. Assuming that it would be fraudulent to publish such a claim if it were not true, Jane reasons as follows (for simplicity, we will ignore the reference to London in the advertised claim; this will not affect the point we are making):

P1) Sharemasters is the leading personal investment service.

P3) If I employ a personal investment service, then I should employ the leading personal investment service.

C) If I employ a personal investment service, then I should employ Sharemasters.

This looks to be a deductively valid argument. But this is not quite clear, because PI is ambiguous. What does 'leading' mean, in this context? It could mean (and this is no doubt what the advertisers hope that people like Jane will think it means) that Sharemasters is the most effective personal investment service - that it secures better returns for its clients than other personal investment services. But it could also mean that Sharemasters is the biggest such organisation - in the sense of having the most clients (this is the sense in which McDonald's is the world's leading restaurant); it might even mean that Sharemasters is the most profitable personal investment service - that is, that it makes the most profits for the owners of Sharemasters itself, not necessarily for its clients (after all, this organisation is a business, and profitability can plausibly be said to be the measure of who is the 'leader' in a certain field of business). Suppose now that you wish to evaluate Jane's argument. You are aware of the ambiguity, so you rephrase PI in each of the three ways, yielding three arguments:

P1 (a) Sharemasters secures higher returns for its clients than any other personal investment service.

P2 (a) If Jane employs a personal investment service, then she should employ the personal investment service that secures higher returns for its clients than any other personal investment service.

C) If Jane employs a personal investment service, she should employ Sharemasters.

P1 (b) Sharemasters is the most profitable personal investment service.

P2 (b) If Jane employs a personal investment service, then she should employ the most profitable personal investment service.

C) If Jane employs a personal investment service, she should employ Sharemasters.

P1 (c) Sharemasters is the biggest personal investment service.

P2 (c) If Jane employs a personal investment service, then she should employ the biggest personal investment service.

C) If Jane employs a personal investment service, she should employ Sharemasters.

Now all three arguments are deductively valid. But are any of them sound? First of all consider arguments B and C. Even if we assume that Pl(b) and Pl(c) are true, it does not seem that these are sound arguments, because it does not seem that either P2(b) or P2(c) are true. Perhaps they have some plausibility - since presumably if Sharemasters were highly unsuccessful at making money for its clients, then it would not have grown so big or become so profitable. But these would not be very reliable assumptions; to reason in the manner of C, for example, would be like concluding that since McDonald's is the biggest restaurant in the world, it has the best food.

So you can conclude that Jane's argument has a good chance of being sound only if argument A is what she had in mind. Suppose you investigate, and find that it is true that Sharemasters is the biggest as well as the most profitable personal investment service in London. Suppose you find, however, that it is not the most effective personal investment service in London; its size and profitability are due to its high fees, its organisational efficiency, and effective advertising. Hence Pl(b) and Pl(c) are true, but Pl(a) is false. You must therefore conclude that although it is valid, argument A is unsound. Since neither B nor C seems to be sound, you must conclude that Jane's original argument is unsound; on none of the three possible interpretations does it appear to be sound.

Eliminating the ambiguity of the original argument was crucial in discovering this, for one could very easily think that the original argument was sound. Advertisements of this kind may be said to exploit this sort of ambiguity. If Sharemasters is indeed the largest personal investment service in London, but not the most effective, then the slogan does express something true; yet the advertisers might hope that readers will interpret the claim along the lines of argument A (or possibly along the lines of B, making the questionable assumption that the biggest service of a given sort is likely to be the most effective).

Remember that a primary purpose of reconstruction is to represent the propositions which constitute an argument in the clearest possible way. Thus we should have no qualms about changing the language used to express those propositions; in changing it, we are only trying to gain a better grasp of what the arguer was thinking. There is no guarantee that we will not change or distort the arguer's thinking, but there is no point in allowing ambiguous language to remain unchanged. For we simply cannot evaluate an argument if we do not know exactly what argument we are evaluating. If we simply cannot decide between two interpretations of an ambiguity, then we must give both interpretations of the argument, and evaluate the two arguments independently.

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