Category Archives: Paradox

The Ecclesiastes 1:9 Paradox

If King Solomon were the first one to say:

What has been is what will be,
and what has been done is what will be done,
and there is nothing new under the sun.

it would form a paradox. Err… would be false anyway.


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The Hermeneutical Paradox, or On Being a “Geologist”

I help write curriculum for our church. I play a very tiny role in it. Yesterday the curriculum team leader described our role as being like that of a miner who tries by various methods to find the gems amid the gravel. We get very little space in our lesson plans with which to draw the attention of the end users of our material to the most important elements of a passage. So it has to be efficient. It is very difficult to boil down, say, whole chapters in the book of Exodus into a dozen discussion questions.

To understand some isolated chapters in Exodus requires an understanding of the whole book, which requires an understanding, I’d argue, of the whole of scripture. But an understanding of the whole of scripture should emerge from an understanding of each of its parts (call this the “Hermeneutical Paradox”—also known in the literature as the “Hermeneutical Spiral”).

So our job is to try to gain as developed an understanding of the passage and of scripture as a whole as we can (a lifelong process to be sure), and to try to sift through the “gravel” and find the “gems” of insight in the passage in focus and draw the users’ attention to them through the use of discussion questions.

But here’s the thing. I more naturally perform the role of geologist, as opposed to miner. I am interested in the gravel. I am mesmerized by the strata. The gold is interesting too, but I want it all. So I’d rather be in the field of geology, as it were, than mining. I’d rather indulge my fascination with the breadth and depth of scripture and be rewarded for it than be constrained to pick out just the gems and work only with them.

This is true of my posture toward life as a whole, too—not just toward scripture. I like talking about why some things “are” and some “aren’t”, what causation is exactly, whether humans have minds or just brains, whether free will exists, whether God exists, how species originated, what makes coffee good, what goodness is, whether beauty is objective, etc. etc. I am struck with wonder when I look at just about anything. Wonder and awe. This life and its quirks are simply amazing.

It’s probably good for me to learn to do what I’m learning to do. But someday I will get to go back to school and study philosophy and then get a job as a teacher and get to learn from, share with, teach, and be challenged by this world’s other “geologists”.

Gold-diggers look elsewhere.


Filed under Faith, Paradox, Theology

The Ammonite Paradox

The Biblical prophet Ezekiel says three times that the Ammonites will be remembered no more. I only know about the Ammonites because I read about them in the Bible.

Ezekiel anticipatorily plagiarizes Shakespeare, whose Sonnet “Shall I Compare Thee to a Summer’s Day” ends with the following.

So long as men can breathe or eyes can see,
So long lives this, and this gives life to thee.

Shakespeare’s lines are not quite paradoxical, but form something like a self-fulfulling catch-22 (DCIT). Ironically however, I don’t think anyone knows the identity of the poem’s subject.

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Grandma’s Paradox

The leftovers always fit in a smaller container than you think, even when you take this into consideration.

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Tolstoy’s Paradox

From Ralph Matlaw’s “Tolstoy”:

Tolstoy, who expressed himself on most questions, wrote to his friend, the critic and philosopher Strakhov, that in order to convey in words everything that he wanted to say in Anna Karenina, he would have to write the entire novel over again, and with some irony congratulated those critics who explain in their articles what his work means, assuring them that they know more than he about it. Clearly the statement is no deterrent to those who would analyze Tolstoy’s work, but it does point to an area of inquiry not sufficiently explored: the elaborate and organic design manifest in the smallest detail no less than in the grandiose conceptions and structures that make Tolstoy’s works marvels of conclusion and organization.

Tolstoy anticipatorily plagiarizes Bonini.

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On intuition.

So when I think about logically valid inferences like the fact that if all men1 are mortal and Socrates is a man, then Socrates is mortal, I conjure up the incorrigible belief that they are absolutely certain (when their premises are true). But why, exactly? For any story you could tell me I could ask “why does that make these things certain?”. For example, if you try to explain the rules of deduction, I could simply ask why such rules should have purchase with me2. It would be difficult for me to do this with a straight face however, and without losing you as a friend, but still. I could.

But why do we take the reliability of logic and math for granted?

I think it’s because the veracity of things like simple arithmetic and obviously valid inferences are strongly intuitive. In fact, our intuitions concerning simple math and logic are so powerful that just to understand what it means to add two and two or what it means for something to be true of a class of objects, causes the one who understands to believe that the sum of two and two is four or that what is true of every object in a class is necessarily true of any given object in it. The veracity of the enterprise is simply indubitable for the sane man or woman.

In this way I actually think that intuition is the foundation of reason. I intuit that it is the case that if it is true that P implies Q and you grant P, then Q follows inescapably. Assuming that intuition to be correct, logic can proceed. But there is no independent evidence for the truth of what is being assumed. Any “evidence” you could give me for the reliability of logic and math would assume the veracity of the things you’re trying to prove.

Not all intuitions are this powerful, however. And many of our intuitions turn out to be wrong. Therefore the goal of philosophy is to, with sincerely attempted intellectual honesty and other virtues, iron out our tree of intuitions and what we’ve inferred from them in conjunction with observation, so that there aren’t any kinks in our weltanschauung.

1 That is, those men who are not Elijah, Enoch, Jesus, those to be raptured, or the sheep to be welcomed into the Kingdom.

2 In fact, in every logical inference lies a hidden presupposition that cannot be argued for without infinitely begging the question. Namely, the veracity of logical validity. So when presented with the facts that all men are mortal and Socrates is a man, to believe on the basis of those two facts that therefore Socrates is mortal, assumes that if all men are mortal and Socrates is a men, then Socrates is mortal.

But it gets worse. Let us temporarily grant the assumption that “if all men are mortal and Socrates is a man, then Socrates is mortal”, which permits us to infer that Socrates is mortal, granted that all men are mortal and Socrates is a man. The new meta-syllogism formed by the original in conjunction with the assumption duplicates the same assumption on a higher order: that validity is veridical. It assumes that if it is the case that if all men are mortal and Socrates is a man, then Socrates is mortal, and if all men are mortal and Socrates is a man, then Socrates is mortal!

Similarly to believe on the basis of it being the case that if it is true that if all men are mortal and Socrates is a man then Socrates is mortal, and so if all men are indeed mortal and Socrates is indeed a man then Socrates is indeed mortal, therefore given that all men are mortal and Socrates is a man, then Socrates is mortal after all.

And so on.


Filed under Mathematics, Paradox, Philosophy, Virtue