Several comedians have famously quipped on air, “Can I say [expletive deleted] on radio?”
A paradox is a statement that seems to be inconsistent, roughly “talking around.” The classic is Epimenides’s remark (about 600 BCE) that “All men from Crete are liars.” On the face of it, this might be an overgeneralization, but it is certainly sayable. What made this a paradox is that Epimenides was from Crete. We can wiggle out of the difficulty by differentiating between the sentence “All Cretans are liars” and the statement “Epimenides said ‘All Cretans are liars.’” One could be false and the other true without being contradictory.
Philosophers distinguish between statements (what one person says at a particular time) and sentences (statements that are imagined to be true or false independent of any particulars about saying or knowing). Most of us most of the time go around uttering statements and expecting others to treat them as sentences. And you can quote me on that.
Philosophers have a different name for the tough cases. An antinomy, which in Greek literally means against the law, is a sentence where each part is meaningful but the parts together mean something else. Here are some of my favorites:
- This is the short end of the stick.
- Pull yourself up by your bootstraps.
- Is it hotter in Florida or during the summer?
- The Cheshire cat slowly disappeared until nothing was left but a smile.
- I will set the meeting after Tuesday but before Wednesday.
- My brother is an only child.
- I believe; help thou my unbelief (Mark 8:24).
- The square root of minus blue is insoluble when dancing the phlebotomy.
- The clean shaven Barber of Saville shaves everyone in Saville who does not shave himself.
Here are a few antinomies of a more serious nature:
- Thought is a conscious neural process, although I am never conscious of any neural activities taking place.
- Individuals with finite knowledge should act only on the basis of universal ethical principles.
- My personal identity is the part of me that does not change, which I only see now that I am older and wiser.
- We can all agree on what is best if we just recognize our differences.
It would be an antinomy in high heels to say “I could not decide whether the antinomy was true or false.” Antinomies make a point about a situation, like smiling or filibustering. But they are not intended to be claims about the world. They are metaphors and make commentaries that cross at least two levels of meaning. The Cheshire cat reminded Alice and us that we are in Wonderland. Russell’s Paradox about the Barber of Saville illustrated that set theory is inherently inconsistent. Some antinomies are just silly things we say in hopes others will mistake us as being profound or not to lose our place in the conversation.
Antinomies are emergent in the sense of being about (meta) but not reducible to their parts. As Nietzsche remarked, “Truth is a mobile army of metaphors.”