What is wrong with our thoughts?

That is the title of the final chapter in a wonderful collection of essays by David Stove in his book The Plato Cult and Other Philosophical Follies (Basil Blackwell, 1991).

Stove includes a list of 40 wrong statements in this chapter and asks us to identify what exactly is wrong with them. His claim is that each of these statements is wrong in a different way and that we need a nosology (study of diseases) of human thought to be able to identify the different types of errors (except perhaps for the errors in the first two statements). Stove also thinks that such a nosology will be either too long or too short to be useful.

All statements have a common thread of the number three (mostly for its humor value). If you are puzzled by the strangeness of these statements, I suggest that you read Stove's book to understand why he makes them.


What is wrong with these statements?

  1. Between 1960 and 1970 there were three US presidents named Johnson.
  2. Between 1960 and 1970 there were three US presidents named Johnson, and it is not the case that between 1960 and 1970 there were three US presidents named Johnson.
  3. God is three persons in one substance, and one of these persons is Jesus, which is the lamb that was slain even from the foundations of the world.
  4. Three lies between two and four only by a particular act of the Divine Will.
  5. Three lies between two and four by a moral and spiritual necessity inherent in the nature of numbers.
  6. Three lies between two and four by a natural and physical necessity inherent in the nature of numbers.
  7. Three lies between two and four only by a convention which mathematicians have adopted.
  8. There is an integer between two and four, but it is not three, and its true name and nature are not to be revealed.
  9. There is no number three.
  10. Three is the only number.
  11. Three is the highest number.
  12. Three is a large number.
  13. Three is a lucky number.
  14. The sum of three and two is a little greater than eight.
  15. Three is a real object all right: you are not thinking of nothing when you think of three.
  16. Three is a real material object.
  17. Three is a real spiritual object.
  18. Three is an incomplete object, only now coming into existence.
  19. Three is not an object at all, but an essence; not a thing, but a thought; not a particular, but a universal.
  20. Three is a universal all right, but it exists only, and it exists fully, in each actual triple.
  21. Actual triples posses threeness only contingently, approximately, and changeably, but three itself possesses threeness necessarily, exactly, and immutably.
  22. The number three is a mental construct after all, a convenience of thought.
  23. The proposition that 3 is the fifth root of 243 is a tautology, just like An oculist is an eye-doctor.
  24. The number three is that whole of which the parts are all and only the actual inscriptions of the numerals, three or 3.
  25. Five is the same substance as three, co-eternal with three, very three of three: it is only in their attributes that three and five are different.
  26. The tie which unites the number three to its properties (such as primeness) are inexplicable.
  27. The number three is nothing more than the sum of its properties and relations.
  28. The number three is neither an idle Platonic universal, nor a blank Lockean substratum; it is a concrete and specific energy in things, and can be detected at work in such observable processes as combustion.
  29. Three is a positive integer, and the probability of a positive integer being even is 1/2, so the probability of three being even is 1/2.
  30. In some previous state of our existence we knew the number three face-to-face, as it is in itself, and by some kind of union with it.
  31. How can I be absolutely sure that I am not the number three?
  32. Since the properties of three are intelligible, and intelligibles can exist only in the intellect, the properties of three exist only in the intellect.
  33. How is the addition of numbers possible? Nothing can make the number three into four, for example.
  34. What the number three is in itself, as distinct from the phenomena it produces in our minds, we can, of course, never know.
  35. We get the concept of three only through the transcendental unity of our intuitions as being successive in time.
  36. One is identity; two is difference; three is the identity of, and the difference between, identity and difference.
  37. The number three is not the ideal object of intellectual contemplation, but a concrete product of human praxis.
  38. The unconscious significance of the number three is invariably phallic, nasal, and patriarchal.
  39. The three members of any triple, being distinct from and merely related to one another, would fall helplessly asunder, if there were not some deeper non-relational unity of which their being three is only an appearance.
  40. It may be---though I don't really believe in modalities---that in some other galaxies the sum of three and two is not five, or indeed is neither five nor not five. (Don't laugh! They laughed at Christopher Columbus, you know, and at Copernicus; and even the logical law of excluded middle is being questioned nowadays by some of the sharper young physicists).

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