The Troubled Tortoise

http://www.philosophyexperiments.com/tpm/Paradoxes5.aspx

Thomas Morrison, a philosophy writer in Kansas City, Missouri, wrote for Epoché Philosophy Monthly of March 2019:

“The profound thinker known as Lewis Carroll made enormous strides in both the imagination and in mathematics and logic. In an 1895 issue of Mind we are exposed to a masterful display of both at once. Carroll writes a three-page scene in which Aesop’s famous tortoise questions the Homeric hero Achilles on the foundations of logic. In effect, he asks: if I accept as true that ‘All As are Bs’, and that ‘This is an A’, why must I accept that ‘It is a B’?
I am following Carroll’s exposition itself in construing logical consequence as a matter of truth (semantic consequence), and not provability (syntactic consequence).

I will discuss what I believe are the two important lessons that the troubled tortoise taught us: one about logic and one about ourselves.

We begin with Carroll flouting Zeno’s racetrack paradox. Clearly he accepts an implicit argument against it and must so for we see Achilles and the Tortoise at the end of the race. The hero is asked by the Testudine to consider a subtler ‘race course’ that, unlike what many believe, is in fact impossible to traverse. This infinite series is the logical syllogism…

…All of this is to say that logic and human life will always exhibit a separation. Carroll’s puzzle is not a problem for logic per se as it is a problem for the tortoise qua conscious individual. It is the problem we all have of wanting to be forced or compelled; of wanting something in lieu of the indifferent void that meets us at every present; hence magic words; hence prayer; hence language. The rabbis of the Talmud believed in the mysterious power of language to create reality. Consider the narrative of the Golem in Jewish folklore: a creature sculpted from mud is brought to life by inscribing a word on it, such as emet (Hebrew for “truth”). The creature becomes unruly, its master removes the word, and the monster returns to dust. Or consider John 1:1 from the New Testament, “In the beginning was the Word, and the Word was with God, and the Word was God.” And consider magic words. “Abracadabra” is Arabic for, “I create as I speak.” This phrase was written on the clothing of Roman soldiers in the 3rd century to prevent malaria (Champlin 1981). And again it was put on the doors of Londoners in the 17th century to resist the plague (Defoe 1911). We have a very deep-seated desire as human beings to have a connection between world and word. We want words to change reality. And we don’t have to go very far for a proof — albeit a far shallower boon than magic promises. This essay is its own proof. It’s the very idea of communication. And for the sake of science, politics, and everyday life, we hope that we can actually change peoples’ minds by reasoned argument. But, nevertheless, as we have shown, logical arguments can no more force a rock to fly upwards than they can force a person to think anything. As Dostoevsky’s underground man exclaims in the heart of duress, “It may be the law of logic, but not the law of humanity” (Ch. 9). In light of the magazine title Epoché it would be wrong of me to fail to mention the connection with this notion and that of the ability to suspend the world, or doubt, or the epoché, as utilized in 20th century phenomenology. The reason I do not explore this further is that although this separation between human life and logic smacks of the epoché, the notion of non-transgressable logical laws alluded to with Aristotle’s help above would not sit nicely in a Sartrean ontology, for example.

So what did the troubled tortoise teach us? In this quick, three-page scene we are exposed to two very important lessons in the nature of logic. First, that logical implication is something quite different than a proposition to be accepted. And second, that human reality can always ask “ and why must I?”.”

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