Tuesday, June 12, 2012

Concepts and Objects

The logician Gottlob Frege defined concepts as functions that take objects as arguments to yield truth-values. That sounds more difficult than it really is. Consider the function "x + 3", which lets you put a number in the place of x to yield a numerical value. So if x = 7, the function yields 10 as its value. Now consider the function "x is a horse". What Frege suggested was that if you put various creatures in the place of x then the sentence will become either true or false. "Smarty Jones is a horse" is true, while "Thomas Basbøll is a horse" is false, Just as "7 + 3" is 10, while "5 + 3" is 8. The same function yields different values when given different arguments. When the value of a function is either true or false then the function is a concept and its arguments are objects.

One of Frege's most fascinating contributions to modern philosophy was the idea of a Begriffsschrift, a "conceptual notation". He tried to develop a way of writing our concepts down in such a way that their truth-functionality, if you will, could be easily surveyed. Unfortunately, it looked like this:

(Source: Frank Hartmann)

My hope is that our prose can approach the (logical) clarity of this kind of presentation while overcoming its (epistemic) austerity.

One way to test your prose for clarity is to ask yourself what concepts and objects are distributed on the surface of the page. Just as there will be a finite number of paragraphs (and, therefore, a finite number of knowledge claims), there will be a finite number of concepts and objects. You should be able to make a complete list of the conceptual and objective content of your text. You should even be able to extend that list to include some of the concepts that are relevant to the named objects but are not at work (functioning) in your text, and some of the objects that are not named in the paper but nonetheless yield true statements when the concepts that are at work in your paper take them as arguments. All this will help you realize the promise of what Frege called "perspicuity" (Übersichtlichkeit) on "the two-dimensional expanse of the writing surface". Even in prose.

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