The Kōans of Gottlob Frege

It might seem an odd claim, but Emmanuel Levinas (Continental philosopher par excellence; and Jewish) and Gottlob Frege (Analytic philosopher par excellence; and anti-Semitic) have large things in common:

• They are both hedgehogs - rotating, stretching and hammering their single peg into every hole presented to them. Levinas' peg is an Absurd kind of agápē; Frege's is the logical-componential bedrock of reality.



• They are both wildly successful in tiny alleyways of the academic endeavour.
  


• And most of all in that both of their systems feel dishonest, at first and maybe after. This is ironic, because their strategies are I think conceived in the spirit of truth. Frege is sometimes more of an accountant than a philosopher: his sneaky mathematical abstraction lets him bypass controversies... but led to the rise of Analysis and a sleek metaphysical minimalism which only recently ended its reign. Levinas' gnomic, logic-free Proclamations... are perfectly appropriate in his anti-ontology anti-phenomenology world, built as it is of neurotic and unimaginable love.

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A kōan is a melodramatic tool of Zen Buddhism* by which a master presents an acolyte with an apparently nonsensical or paradoxical story and the acolyte has to go off and solve it. (A flash of prajna does the trick.) Frege uses existing words for very new and idiosyncratic philosophical purposes. Taken with his highly repetitive and recursive structure, this makes his system humorous if viewed aesthetically (i.e. in itself as writing) rather than looked 'through' to his meaning.

* Or at least our Hollywood version of it.

(NB: I know that the following are not strictly kōans; that's the joke. The essence of a kōan is that it is not logically analysable. And whatever else Frege is, he is that!)

1. Frege say: ALWAYS SEPARATE WITH SHARPNESS THE PSYCHOLOGICAL FROM THE LOGICAL.

2. Frege say: NEVER LOSE SIGHT OF THE DISTINCTION BETWEEN CONCEPT AND OBJECT.

3. Frege say: NEVER ASK FOR THE MEANING OF A WORD IN ISOLATION, BUT ONLY IN THE CONTEXT OF A PROPOSITION.

4. But Frege also say: THE NOMINATUM OF THE SENTENCE IS A FUNCTION OF THE NOMINATA OF THE NAMES OCCURRING IN IT (!)

5. Frege say: FUNCTIONS ARE IDENTICAL IFF THEY HAVE THE SAME EXTENSION.

6. Frege say: NUMBERS ARE OBJECTS; NUMBER IS A SORTAL CONCEPT.

7. Frege say: A NUMBER IS AN OBJECT OF THE EXTENSION OF A CONCEPT OF A CONCEPT.

8. Frege say: CONCEPTS SHARE A NUMBER IFF THEIR OBJECTS ARE EQUINUMEROUS.

9. Frege say: EQUINUMEROSITY IS AN EQUIVALENCE RELATION.

10. Frege say: ABOUT THE INFINITE NUMBER ∞ SO DEFINED THERE IS NOTHING MYSTERIOUS OR WONDERFUL.


0. Frege say: ZERO IS THE EQUIVALENCE CLASS OF CONCEPTS LACKING OBJECTS IN EXTENSION.



I once quarreled with a friend about logic. I insisted then that logic was about nothing - that once it had been the study of winning arguments, but was now merely the hardest game in the world. This was unfair (though not untrue).

Some tasks of logic:

1. To discover supremely general truths, and bear our scepticism and hand-waving stoically.



2. To make an inventory of forms, and thereby see how low and far we can take thought and what shapes good thought can have.



3. To investigate necessity, particularly necessary interdependencies between claims, and thereby show us the hundred puppet-strings each thought has.



4. To try and give mathematics a seat; she's been standing all day.



5. To preserve what little truth we have; ferry it in sound containers, and cry over spilled value.