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Reconcile ourselves with the irreconcilable May 25, 2013

Posted by Ezra Resnick in Ethics, Religion.

In the Huffington Post, Rabbi Shmuley Boteach opines that to claim the Holocaust was punishment for sin is “ignorant, repulsive, and wrong.” Also, “abhorrent” and “factually absurd.” Moreover, those who make such arguments aren’t doing God’s reputation any favors:

Let’s say for a moment that they’re right. God bears no responsibility for the gas chambers at Auschwitz because the Jews of Europe had it coming. They earned death by virtue of their iniquity. They deserved to be turned into ash because they had abrogated God’s covenant.

Now, how many of you feel like praying to a God who could do that? How many of you feel like loving a God who enacts the death penalty for eating a cheese burger? How many people would want to worship a God who cremates children when their parents drive on the Sabbath?

Good point! I wonder where anyone could possibly have gotten the “abhorrent” idea that God would do things like that… Well, I guess there is this:

But if ye will not hearken unto Me, and will not do all these commandments; and if ye shall reject My statutes, and if your soul abhor Mine ordinances, so that ye will not do all My commandments, but break My covenant; I also will do this unto you: I will appoint terror over you, even consumption and fever, that shall make the eyes to fail, and the soul to languish… And if ye walk contrary unto Me, and will not hearken unto Me; I will bring seven times more plagues upon you according to your sins. And I will send the beast of the field among you, which shall rob you of your children, and destroy your cattle, and make you few in number… And ye shall eat the flesh of your sons, and the flesh of your daughters shall ye eat…

And this:

Ye shall keep the sabbath therefore, for it is holy unto you; every one that profaneth it shall surely be put to death; for whosoever doeth any work therein, that soul shall be cut off from among his people.

And this

for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate Me;

But if, like Boteach, we choose to ignore the main theme of the Bible, and maintain that God is worthy of love and worship, surely the only position left available is that God is incapable of influencing our world at all — because horrible things happen to innocent people every fucking day. I mean, it wouldn’t make any sense to give God credit for the good things that befall us, while absolving him of responsibility for the bad things! Right?

I don’t know why God allowed the holocaust. Nor do I care. Any explanation would not minimize the horror of it. Nor would it bring back my six millions murdered Jewish brothers and sisters. Indeed, asking for an answer is itself immoral insofar as it is an attempt to reconcile ourselves with the irreconcilable. What we want is for God to fulfill his promises to the Jewish people, that they might live a blessed and peaceful existence, like so many other nations that are not perennial targets for genocide.

True, God has sustained us, for the most part, and we alone have survived from antiquity. We are grateful to God for our longevity. But it should not take the deaths of innocent Israeli soldiers to guarantee our survival.

It is high time that God show Himself in history and bless a people who have been, for the past three thousand years, the most devoted and religious of nations, deeply faithful to God, practicing charity, promoting scholarship, fostering hospitality, and spreading light and blessing to all nations of the earth.

High time, indeed. In fact, if God doesn’t show himself soon, some skeptical-minded individuals might interpret the consistent lack of divine intervention in our world as evidence that he doesn’t exist at all! Like, for instance, this Oklahoma woman whose home was ravaged by a tornado: CNN’s Wolf Blitzer told her she’s “blessed,” then asked her if she “thanked the Lord.” She replied that she’s an atheist.

Rabbi Shmuley doesn’t know why his God allowed that tornado to kill two dozen people, including ten children; nor does he care. Indeed, he considers asking for an answer to be itself immoral. Nevertheless, he continues to pray for God’s blessings and to thank him for lovingly sustaining us. For the most part.

By way of contradiction May 5, 2013

Posted by Ezra Resnick in Logic, Math.

contradictionAn indirect proof (or proof by contradiction) establishes the truth of a proposition by showing that the proposition’s negation implies a contradiction. For example, we can indirectly prove that the square root of 2 is irrational (i.e., it cannot be expressed as a ratio a/b where a and b are integers) by assuming the opposite — that √2 can be expressed as a ratio of integers — and showing that such an assumption leads to a contradiction (e.g., that b is both even and odd).

Some people find indirect proofs unsatisfying, or even a bit suspicious: it feels like we’ve been cheated out of understanding why the proposition is true. Direct proofs seem more intuitive and dependable. This raises the question: Does every proposition that can be proved indirectly have a direct proof as well? Or are there propositions that can be proved indirectly, for which no direct proof exists?

Before attempting to answer that question, let us first consider this humble proposition:

(p) This proposition cannot be proved directly.

We can prove proposition p is true — indirectly. Start by assuming the opposite, that is, assume there exists a direct proof of p. In particular, that means p is true. But p states that there is no direct proof of p — contradicting our assumption. So our assumption must be false; hence p is true.

Let us now attempt to prove the following proposition:

(q) Not all propositions that can be proved indirectly can also be proved directly.

We shall prove the truth of proposition q (you guessed it) indirectly. Assume the opposite: that is, assume any proposition that can be proved indirectly can also be proved directly. Then, since p can be proved indirectly (as demonstrated above), there must also exist a direct proof of p. However, the existence of such a proof contradicts (the proven) proposition p! So our assumption must be false — and q is true.

Ah, but the question remains: Can q be proved directly?