On Truth and Probability

In “A Grammar of Dissent: Flatland and the Theology of Probability,” Baker, Berkove, and Smith use Edwin Abbott’s Flatland to expound upon the intellectual feud between Abbott and John Henry Newman, in which the two had stark differences in their perceptions of both science and religion. Newman’s claim was that miracles do exist in such a way that reasoned explanations of proposed miracles do not discredit the existence of miracles as phenomena. Abbott was a skeptic, and so he did not believe those things which had no evidence of their happening; reason and imagination were the primary conduits through which knowledge was attained. For Abbott, imagination is the basis for all knowledge, but reason refines imagination to truth by winnowing away falsities[1]. On the contrary, Newman used reason to confirm his imagination, in what we would call today confirmation bias. In terms of Flatland, the perception of a circle as a circle, round and edgeless, is an illusion; it is a myth which connotes, for Abbott, the truth that a true circle probably exists, but not in the form of the many-sided polygon. Newman would, also, imagine that there’s a circle, and that the circle is actually a many-sided polygon. Yet, where the two men differ is here: Newman believes that, as something asymptotes towards a truth, though never reaching it in certainty, there is a sort of mental certitude that conforms to the imagination.  It is Newman’s imaginative excess that goes beyond the scope of what is present and making conclusions upon the sightless.

Baker et al. make three perceptions of Flatland[2]:

  1. A Square and the King of Lineland are wrong to declare impossibility of higher dimensions, but not to be skeptical of them.
  2. Both A Square and the King are right to try to account for their strange experiences with natural rather than miraculous explanations.
  3. A square is both right to reject the Argument from Analogy prior to his physical experience of the third dimension and wrong to imply it so uncritically after that experience.

We see A Square using inductive reasoning’s, periods of skeptical inquiry, while listening to the Sphere, but he also fails at the outset. The authors bring up the passage on page 106 of Flatland:

In that blessed region of Four Dimensions, shall we linger on the threshold of the Fifth, and not enter therein? Ah, no! let us rather resolve that our ambition shall soar with our corporeal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth -.[3]

A Square moves from a period of inquiry where his imagination is mitigated by his reason to an exercise of pure imaginative excess, concluding that because he saw the first dimension, because he dwells in the second dimension, and because he has perceived the third dimension, there exist innumerable dimensions, each far greater and more divine than the lower. The flaw of A Square is that he ascertains certainty from probability. And so, Baker et al. argue that Flatland is a tale of warning to those whom trek into the realms of uncertainty, to always remain on the edge of truth, and to always be humble in the face of argument, for you might learn something.

With regards to the article, I agree with Baker, Berkove, and Smith. Flatland is a tale of discovery; it is a sort of moral fable. It reflects the more human qualities of ourselves in how we deny the possibility of certain things, questioning them at first, but also how easy we are carried away by imagination, how easy it is for us to leave reason in the dust. It’s easier to accept answers that conform to one’s preconceptions, but for many, including myself, it’s humbling to know that we don’t know. In a way, it elevates us out of ‘pointland.’


[1] (Baker, Berkove and Smith) 4.

[2] (Baker, Berkove and Smith)5-6.

[3] (Abbott)106.

B. Keiser

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