A recent report in The Independent about the Chocolate Digestive reported as follows on a passage from a United Biscuits email (United Biscuits are responsible for producing the prestige brand of Chocolate Digestive):

“For your information,” a spokesperson wrote, “the biscuits go through a reservoir of chocolate which enrobes them so the chocolate is actually on the bottom of the biscuits and not on the top.”

The Independent reported the story as “serious snack news.” And if the report were substantiated, they would be right. For the biscuits have ordinarily been presented and consumed chocolate-side up since they were first produced in 1925.

However, further reflection reveals that the report goes beyond the evidence in significant ways. Crucially, it does not follow from the fact that chocolate is applied from below that the side to which chocolate is applied is the base. Suppose, for example, that cars had their roofs painted by the same method; that would not lead us to accept that we had been driving them upside down. Additional grounds would be required, therefore, before it could be established that the biscuits are chocolate bottomed rather than topped. Furthermore, it does not follow merely from the decision of United Snacks, or individual employees thereof, that the biscuits are chocolate based. Compare again: were Toyota to claim that their cars are being driven upside down, it would—happily—not make it the case.

However, despite its indecisiveness, the report raises interesting and delicate issues. First, could there be a fact of the matter about the correct orientation of the Chocolate Digestive? Second, if there could be, could we be universally, or near-universally ignorant, of the facts? (The aficionado will recognize that an affirmative answer would sustain a form of epistemicism about correct biscuit orientation.) Third, and related, are Chocolate Digestives handed: that is, could universes differ only in that one universe contains only chocolate-up Digestives, while the other contains only chocolate-down Digestives? (The issues are recognizable related to those about incongruent counterparts that were discussed by Kant in his 1768 essay, ‘Concerning the Ultimate Foundation of the Differentiation of Regions of Space’.)

(For further information about the Digestive biscuit, and Chocolate Digestive, see the Wikipedia entry. The entry cites the following passage from Encounter, volume 50: “A government-appointed group of scientists, the Food Standards Committee, is to study the term “Digestive biscuit”, which has been used since the reign of Queen Victoria. The committee is to decide whether the term should be banned on the ground that it implies that the biscuit eats itself.”)


Star Wars story 1

A long time ago in a galaxy far, far away lived Princess Leia, her father Darth Vader, her brother Luke Skywalker, and her mum Queen Amidala. Darth Sidious had taken over all the world, but the only place that wasn’t crashed down was the palace where Queen Amidala lived, so the rebels decided to tell her why they came to stay at her palace. But, oh no, they’ve discovered that Darth Vader is a real live baddie! But Princess Leia knows what to do. She asked Queen Amidala and Han Solo to get their blasters out and they shoot all the baddies. The baddies got their lightsabers out but the rebels shot them first, so the baddies couldn’t get the rebels. And the planets came back. The End.

Our special planet

Planet name: Jewel

What’s special about Jewel? When you got to the planet you can take all the jewels, because they don’t turn to rock when you take them from the planet. If you go there, you get to play with your own little child. The children like to play with the jewels. They like to put them in bags so that they can take them home. Every jewel is blue, or pink, or purple. If you take one of the jewels, you have to be very careful that you don’t break any of them.

Alonzo Church was a very important figure in 20th Century philosophy, especially at its intersection with mathematics. For example, he was pivotal in articulating what has come to be known as the Church–Turing Thesis. (On one formulation, the thesis has it that every computation meeting certain conditions—in technical parlance, every mechanical or effective computation—can be carried out by a Turing Machine (a specific type of simple computer).)

Key to the articulation of that thesis was a certain approach to philosophy, involving a combination of reflection, formalisation, and further reflection. To a first approximation, the approach involves initial reflection on the target subject matter, followed by formalisation so that a determinate theory of part of the subject matter is produced, followed by further reflective testing of the theory and then its re-formalisation, its rejection, or (though this is rare) its provisional acceptance. The role of formalisation—provision of a determinate theory—is to facilitate testing of the theory by making as explicit as possible its connections with other theories and claims, and more generally by making as explicit as possible its pattern of commitments. Clarity about those commitments can then facilitate the generation of testable predictions. Although the outputs of reflection are accorded weight in this kind of procedure, both in producing and in testing theories, none is taken to be sacrosanct: the aim is optimal capture of the fruits of reflection, and that might involve the sacrifice of putatively self-evident darlings.

It’s not implausible to see the approach, at least from a certain height, as an attempt to pursue philosophy via something like the methods that have achieved success in pure mathematics. (At least, that is so if we are willing to allow that little or nothing in pure mathematics is transparently self-evident and, so, immune from potential rejction.) Furthermore, Church himself suggests that, from the same sort of height, the method bears comparison with approaches pursued in the empirical exact sciences. Here, for example, Church sketches a notion of observation that aims to be neutral between the respective outputs of perception and reflection:

“But the preference of (say) seeing over understanding as a method of observation seems to me capricious. For just as an opaque body may be seen, so a concept may be understood or grasped. And the parallel between the two is indeed rather close. In both cases the observation is not direct but through intermediaries—light, lens of eye or optical instrument, and retina in the case of visible body, linguistic expressions in the case of the concept. And in both cases there are or may be tenable theories according to which the entity in question, opaque body or concept, is not assumed, but only those things which would otherwise be called its effects.” (Church, ‘The need for abstract entities in semantic analysis’, American Academy of Arts and Sciences Proceedings, 80, 1951: 100–113.)

Church’s model appears to be approximately this. Opaque bodies present a plurality of appearances to sight, mediated by light, &c.. And theorising about such bodies is, in part, a matter of seeking the underlying principles that organise the appearances. In seeking such principles, we may begin by attempting to capture all the appearances. However, it is likely that the pursuit of optimal theories—theories that are maximally simple, general, elegant, &c.—will lead us to view some of them as mere appearances. Similarly, concepts present a plurality of appearances to the understanding, mediated in this case by language. And theorising about concepts is, in part, a matter of seeking the principles that organise those appearances.

Before we can get into a position properly to assess Church’s proposal, two natural questions of clarification are these. First, how exactly are we to understand the correlative notion of appearances in the case of the understanding? Are these particular judgments, or intuitions, or something else? Second, how should we think of the analogy between the role of media in sensory perception—that is, the role of light, eye, and instrument—and the role of language in the operations of the understanding?

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