Archive for June, 2013

Liar paradoxes, a problem with reductio proof and speech acts

June 20, 2013

It’s easy to mistake paradoxical sentences for liar paradoxes. “If this sentence is true, then it is false,” is a liar paradox. If the sentence is true, then the antecedent is true. If the antecedent is true, then the consequent must be false, the implication as a whole is false, so the sentence must be false. So if the sentence is true, then it is a contradiction and a falsehood. So the antecedent must not be true. If the sentence is false, antecedent is false, and the implication as a whole is true.

“If this sentence is false, then it is true,” however, is not a liar paradox. If it is false, then the antecedent is true and the implication fails, and the whole is false. If the sentence is true, then the antecedent is false, the implication holds, and the sentence is true. That’s not a paradox, it’s just a sentence the truth of which cannot be determined. It’s like the sentence, “This sentence is true.” Is it true or false? How could you tell?

Similarly, “The sentence I am now writing is true,” is indeterminate. “The sentence I am now writing is false” is provably a liar paradox, athough one could ask of these two sentences “true or false of what?” The deductive proof that yields a liar paradox of the latter, is a reductio: assume the sentence is true, you deduce that it is false; assume it’s false, you deduce it’s true. So if it’s true, it’s false and vice versa. But if you ask “true of what?” then you’re asking for an empirical answer — does the sentence corresponds to something, in this case to its own truth. Is truth a thing that can be pointed to? If it’s a correspondence with something, we’re stuck in an infinite recursion. So these sentences, on the one hand, lead to a questioning of the correspondence theory. But they also lead to questioning of the validity of deductive reductio argumentation, not unlike that questioning of the reductios that led Cantor to multiple levels of infinities, and the intuitionist rejection of the reductio in favor of proof by demonstration. Several directions from here: you can say these sentences don’t correspond to anything; or correspondence is not complete; or correspondence, even with its incompleteness is a better option than reductios that lead to liar paradoxes.  (more…)

Advertisements

Intended paradox

June 16, 2013

“I’m very witty!” someone wrote in a comment box in response to the criticism “You have no wit.”

“I’m very witty” might seem at first a witless and therefore unpersuasive response, unless it is sarcastic, in which case it is actually witty. If it’s sarcastic, the meaning intended to convey is that author isn’t witty, and therefore it implies that the comment itself also is not witty. The joke is, the author knows it’s not witty; yet that’s what makes it witty. So if it’s witty, it’s a lie; if it’s a lie, it’s not witty: a liar paradox.
But if the comment is merely false, then there’s no paradox — just a reply by someone who thinks he’s witty but is too dull to know he’s not witty, and hasn’t enough wit to say so wittily.
So if it’s a lie, then it is a meta-witty paradox; if an honest falsehood, it’s just stupid.

What’s interesting is that the intention or speaker’s attitude or character of mind induces the paradox, not the words alone. The paradox depends on who’s speaking, liar or dolt, wit or fool.

At what price?

June 7, 2013

It’s supposed to be well-established that commodity prices are the inverse of interest rates. Interest rates are as low as they can be and luxury housing prices in NYC are high, for example, and the stock market is flying too. But the rest of the economy is not wildly inflated. Why?

Easy money (low interest rates) flows into commodity inventories (we saw that leading up to the Arab Spring), on the one hand, and on the other, it curbs extraction of new resources and commodities because the low interest rates reduce their monetization, or so the theory goes. Yves Smith posted on it back in 2008:

http://www.nakedcapitalism.com/2008/03/falling-interest-rates-explain-rising.html
Here are the originals:
http://www.hks.harvard.edu/fs/jfrankel/CP.htm
http://www.hks.harvard.edu/fs/jfrankel/CampbellM&CPnberNov.pdf
http://www.federalreserve.gov/pubs/ifdp/2012/1065/ifdp1065r.pdf

That easy money/low interest rates leads to inflation has been orthodoxy since Friedman at least. It was Volcker’s successful program to curb inflation by increasing interest rates, causing a recession, and Bernanke’s opposite strategy to take us out of recession, allowing inflation. But it also has a specific reflex in commodity prices. QE2 caused a global price hike in food prices as investors left the dollar for commodities, that caused the Arab Spring. Not exactly what Bernanke anticipated. His response was washing his hands: other nations have to deal with their own inflation, he quipped, cynically, I thought.