ARGUMENT BY ANALOGY

Philosophical analogies approximate the form of mathematical proportions and therefore might appear to be tight deductive systems. For example, A is to B as C is to D has the same form as 1/2 = 2/4, but the "numerators" and "denominators" of philosophical analogies are never mathematically identical. This ultimately makes mathematical proportions and philosophical analogies quite different. (See the difference between parallel and analogical arguments below.) It makes them inductive arguments, an argument that does not lead to necessary truths. Only deductive arguments give us truths that are true in all cases and without exceptions, e.g., the truths of logic, math, and geometry.

In assessing the value of philosophical analogies, we must ask two questions: Are the things compared similar? and are the things similar in the particular respect in question? If these two questions can be answered in the affirmative, then a convincing argument from analogy probably exists.

In his book Practical Logic, Monroe C. Beardsley contends that there is no such thing as an argument from analogy. "Analogies illustrate, and they lead to hypotheses, but thinking in terms of analogy becomes fallacious when the analogy is used as a reason for a principle" (p. 107). Beardsley does, however, give a good example of an analogy which is "strong" and which can be used to represent one thing as another. This is the analogy of a map: "The dots on the map are not very much like actual cities, and the lines on the map are not all like mountains or wet like rivers.... But the structure of the map, if it is a good one, corresponds to the structure of the country it represents. That is, the shapes of the states are like the shapes on the map; ...and the relative distances between actual cities are like the relative distances between the dots on the map" (p. 106). It is clear that such analogies can be very helpful in clarifying the form and structure of some arguments, even to the point of discrediting a specific argument.

A parallel argument: all elements are equal or similar in all essential particulars;

Or at least identical syntactical elements in corresponding positions.

Analogies have neither of these features.

Mathematical ratios are perfect parallel deductive arguments.