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Frege’s puzzle about identity is a problem presented by the semantics of singular terms. The problem arises when a given object or phenomenon is attributed to more than one singular term. While the terms are not necessarily synonymous, they can be arranged in statements that presuppose their synonymous nature. The most common example is Hesperus and Phosphorus, two names of stars used by the ancients (“Gottlob Frege”). While the definitions are different, the available astronomical data suggests that they represent the same object. In other words, the similarity between the terms cannot be established based on reflection alone (since the information does not appear to be non-trivial) and requires additional empirical evidence (e.g. astronomic observations).
As a solution to the problem, Frege suggested that definitions have two levels of meaning. The first is a reference – an apparent characteristic of an object. The second is since – the way of the presentation of an object, also known as the mode of presentation. In the example of Venus, the terms Hesperus and Phosphorus have the same reference since they refer to the same object but bear different senses since they involve different characteristics of an object (e.g. the time of the appearance in the sky).
Frege’s solution to the puzzle contains several controversial points. First, it relies on the uniformity of both reference and sense. However, since the meaning of some terms is a contingent truth, the latter can differ depending on the individual who uses them. Next, certain concepts that are analytic according to Frege’s definition do not require empirical inquiry and are considered a priori knowledge. Finally, some statements exist that cannot be conclusively defined as either analytic or a priori due to their different senses.
“Gottlob Frege.” Stanford Encyclopedia of Philosophy, 2012. Web.