Frege and MetaphorSteve Kemple

In “On Sinn and Bedeutung”, Gottlob Frege discusses the relationship between signs and objects. He argues that real objects (bedeutung) can be understood in terms of the way we already organize ideas, forming relationships that have the ability to be analyzed in terms of logic. He uses language as a data set, setting up what can be roughly understood as a geometry of words and ideas. I will show that his argument is valid, and that it brings profound elucidation to the way language is used and understood, but will offer one fundamental disagreement.

Frege begins with assertion that in the case of equality (i.e. a = b), the relation is between the actual signs (a and b) as opposed to the actual objects to which they are assigned. He argues that the actual object (bedeutung) to which a symbol (e.g. ‘a’) refers, can be articulated with a variety of symbolic phrases. Regarding a = a and a = b, which as literal objects (ink on paper) are essentially equal in terms of identity, “a difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of the thing designated” (26). He illustrates a triangle with three lines (a, b, and c) connecting its vertices with the opposite midpoint, all three intersecting at the same point. Frege writes, “So we have different designations for the same point, and these names … likewise indicate the mode of presentation; and hence the statement contains actual knowledge” (26). He terms these different but equal statements sinn, or sense.

A bedeutung can be of an object (as in a proper name), or it can be of a proposition. A sentence, Frege argues, can have a bedeutung, in either of these forms (assertoric ones being the former), and one may always be sought. If it is a proposition, the idea can be reduced to truth-value, making every bedeutung either true or false. He then asks if the bedeutung of a sentence will not be changed if part of the sentence is replaced by an expression with the same bedeutung. Through a series of experiments with clausal sentences, he finds that on occasion the initial bedeutung will be changed when an expression with the same bedeutung but different sense is supplanted. He therefore concludes that a = a and a = b, do not necessarily always contain the same cognitive value.

I would argue, in Frege’s support, that the logic he employed is profound beyond the confines of his paper. By taking his argument a few steps further, we can see how a sense of a bedeutung (within a sentence that may or may not contain its own bedeutung) can be incorporated into a larger context of ideas, much as an article or adjective contributes to the bedeutung truth-value of a sentence. The scale may be shifted further, to reveal a much larger (and probably very complex) geometry of ideas. As easily as it was demonstrated by the initial two-dimension illustration of a triangle, the notion of sinn and bedeutung should be similarly applied to n dimensions. For example, the notion of metaphorical truths (or untruths) can be easily deduced from his theorem. In a work of fiction, for instance, there are occasions when the proper names do not themselves contain a bedeutung, but they manage to culminate into something generally regarded as profoundly true (chiefly through employment of sinn). Frege denies this possibility on pages 32 – 33, in the passage regarding Odysseus, and I put that he does so inaccurately.

In conclusion, Frege’s paper does much to elucidate the way we use language, as well as the region between symbols and objects. His proposition is not only profound, but also relevant. His logic piercingly illuminates the way we perceive and communicate, and should be regarded as something other than ink on paper.

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