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December 21, 2014 / 29 Kislev, 5775
 
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Posts Tagged ‘logic’

The Logic of the ‘Winged Pig Conditional’

Thursday, March 14th, 2013

As I’ve mentioned before, I used to teach elementary logic. One of the first topics was compound truth-functional statements, in which the truth of the compound is dependent on the truth of the components. So for example, the compound statement ‘p or q’ is true if and only if either or both of the components, p and q are true.

The definition of the ‘if p then q’ (called a ‘conditional’, and sometimes written p->q) statement seemed counter-intuitive to some students. It is true if and only if either p is false or q is true. That may seem strange, but think about it: suppose I assert that “if I drink 3 cups of coffee then I will have insomnia.” What could falsify this statement? Only one situation: I drink the coffee but still sleep normally.

This definition can be expressed as a “truth table” which tells us what the result will be for every possible combination of truth and falsehood of the antecedent (p) and the consequent (q). Here it is:

p q p->q

True

True

True

True

False

False

False

True

True

False

False

True

Not every conditional statement that we make is a simple function of the truth of its components, but many of them are.

Here is one that I see a lot:

“A majority of Jewish Israelis would give up most of Judea and Samaria, even evacuate settlements, for peace.”

Another way of saying this is that most Jewish Israelis agree with this conditional statement:

“If it would result in a lasting peace, I would support withdrawal from Judea and Samaria.”

The only case in which this statement is false is the one in which the speaker does not support withdrawal despite believing that it would result in peace. So no wonder a majority agrees with it.

It is perfectly rational to accept the truth of the if-then statement, but not support withdrawal because one does not believe that peace would result. For example, many Israelis believe that a withdrawal would result in a Hamas takeover and a Gaza-like situation a few miles from Israel’s population centers. Some point to the PLO’s refusal to recognize a Jewish state with any borders. Others compare the ease with which the Arabs could tear up a peace agreement to the difficulty of repossessing the land after it is ceded.

So clearly the truth of the statement does not imply a readiness on the part of the Israeli public to withdraw; rather it points to a strong desire to finally have an end to the conflict.

But there is more. The truth table above tells us that a conditional is always true when the antecedent is false. In this case, the truth of the consequent is irrelevant. This means that if the antecedent is contradictory or in some way impossible, then the whole statement is always true — but in a trivial sense.

This is what I call a “winged pig conditional.” And that’s what this statement actually is — a trivial one whose assertion commits the speaker to nothing.

I am prepared to bet $1,000 on the truth of the conditional statement “if pigs had wings, then they could fly” (with proper safeguards prohibiting bionic wings, etc.). This is because the antecedent “pigs have wings” is so unlikely as to be considered impossible. So I am not risking any money.

And based on my understanding of the oft-stated intentions of the PLO and Hamas, of Palestinian Arab public opinion, of P.A. and Hamas media, I can say that the proposition that withdrawal would lead to peace is just as unlikely.

To a great extent, the whole idea of a two-state solution as presented by President Obama, Shimon Peres, etc. is a winged pig. Of course it would be wonderful if Israelis and Arabs could live side by side in peace, but since the idea of a Jewish state is so consistently rejected by the Arab side, the questions of “how do we get there” so beloved by Dennis Ross, for example, are so irrelevant as to be uninteresting.

Some years ago, P.M. Netanyahu made news when he announced (under U.S. pressure) that he supported the idea of a Palestinian state in the context of a “two-state solution.” What he meant, of course, was a kind of winged-pig conditional: if the Arabs would agree to recognize Israel as the state of the Jewish people, if the state could be demilitarized, if various security requirements could be met, then …

Of course the response from Mahmoud Abbas was predictable: Netanyahu is lying! He doesn’t support a “two-state solution” because a two-state solution includes right of “return” to Israel for 5 million “refugees,” and no recognition of Jewish ownership of Israel. Not to mention that “Palestine” deserves an army.

This is why the whole “peace process” discussion is so unutterably boring. It is unconnected to reality.

I think that we need to go farther than asking “what do we need to do to get peace?” and even “what do we need for security?” Rather, we must ask “what should the state of the Jewish people be?”

Perhaps those who believe that there is a value to Judea/Samaria that transcends its use as a bargaining chip, and indeed transcends its importance to security, a value that comes from its being the historical homeland of the Jewish people — maybe they have a point?

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Outside the Territory of Reason

Thursday, January 3rd, 2013

As the edge of the fiscal cliff approaches and then recedes, like an imagined desert isle appearing and disappearing admit the waves, the process that has brought America into the tyranny of debt goes on. The national debt, like our annual deficits, is a symptom of the true problem.

Irresponsible behavior is a symptom of irresponsible thinking. Bad choices come from the failure to understand consequences. Power is not just an aphrodisiac, it numbs one to the understanding that there even are consequences.

The centers of people in a nation are the last to feel the cold and their decisions are insulated from their consequences by power and comfort. Even as they warn about the danger, they are too far away from it to truly feel it. It is a shadow to them. An idea. Not a reality.

To the powerful, power is the only reality. And the limits of their own power are unknown to them. The possession of power is a constraint that prevents the possessor from seeing its limits.

We live in a world that has lost touch with the very idea of hard choices. That even in the richest and most prosperous country in the world, you still have to choose one or the other. That you can’t have you cake and eat it too. But as the hard edges of reason have blurred into the haze of wishful thinking, the idea of mutually incompatible choices also fades away. Soon there are no choices, only options.

Our government has vanished into that haze. A haze in which our leaders actually believe that we can be tough and kind, strong and beloved and spending as much as we want without worrying about where it’s coming from. The haze extends to our policies which assume that we can win wars without offending anyone, and spend as much money as we want without recouping it in some way. In a system built on two party stalemates usually broken by compromises, it’s all too easy to believe that you can give and take, without ever having to choose. One or the other.

A country whose leadership does not understand the concept of mutually incompatible choices is doomed to have its political structure decay into tyranny and its economy stagnate and finally collapse. Without the understanding that some choices are hard and fast things, success becomes impossible. When you think that you can do everything, you end up being unable to do anything. When every option is on the table, then no option is on the table. And if the political leadership cannot make those choices, then it will be replaced by another form of leadership that will solve the problem with tyranny. This has happened before. And it will happen again.

The Middle East presents us with the troubling sight of an entire region run by people who are unable to make such absolute distinctions. Princes, sheiks and prime ministers pursue mutually incompatible policies at the same time, make contradictory assertions and often remain unaware that their actions are contradictory. In a region that is outside the territory of reason, everything is always on the table. There is no truth, only layers of lies. Push far enough down and you come away with nothing but hot air. The popularity of Islam as a political solution is due in part to the perception that it represents an absolute certainty. An anchor in a turbulent sandy sea. Not an intellectual anchor of reason, but of fanatical force. The comfort of the thoughtless tyranny of power.

But the West has been headed out of the territory of reason for some time now. Its truths have become ideological beliefs. Its goals have become the self-worship of its own symbols, size for the sake of size, and centralization for the sake of centralization. There is a mingled horror and longing for the savage and the barbaric, as civilization appears to have lost its meaning. The leadership cries “Onward to a united world” on the one hand, and “Back to the caves” on the other. That confused melange boils down to a cultural intelligence which has lost the awareness of its own contradictions. High tech environmentalism, soft wars and valueless money are all symptoms of that same intellectual degeneracy.

Printed from: http://www.jewishpress.com/indepth/columns/daniel-greenfield/outside-the-territory-of-reason/2013/01/03/

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