Consider the theory: 2x > 0. I would say x, may not be positive, thus the theory is wrong. Any non-positive number is a counter example. All I needed was one to disprove the theoy, and I’ve found an uncountably infinite amount.

“QED also requires that you don’t commit the informal fallacy of wrong conclusion: the existence of an exception has little bearing on the likelihood of an outcome.”

There is no likelihood of an outcome as there is no probability distribution. You’d have to make some assumption about what x’s can be chosen with what frequency for me to tell you something about likelihood.

As for your example, I choose E) nothing can be said about likelihood. This is akin to asking, given 1000 randomly selected math problems what is the probability the answer will be positive. It’s a meaningless question, because there is no specified distribution from which we are drawing math problems. If we went to 1000 people on the street, almost all of the math problems would give positive answers. But that tells us nothing about the distribution of problems more generally. In the same way, what is the distribution two people can exist over all possible states and relative frequencies. It is a meaningless question.

The better way to proceed is just to put your assumptions forward first and make sure they prove your argument. For instance, Ricardo assumed two countries, within countries people were identical, across the two countries there were differences. Specifically, one country has an absolute advantage in wool and wine, but the other has a relative advantage in wine. Both countries have full employment and there are no transaction costs or transportation costs across countries. From here, he derives comparative advantage.

It’s an important theory that has earned Ricardo very deserved status in the profession. Does it actually describe the majority of international trade? No, it doesn’t. Under Ricardo’s theory trade comes from differences between countries, and countries specialize almost completely. In the real world, trade occurs most commonly between similar countries trading similar goods (US and Europe selling cars to each other) or countries geographically close (US and Mexico/Canada). So new trade theories evolved that better explained the real world. Does that mean comparative advantage has no effect? No, of course not, it just means its effect is in the context of other factors driving trade.

Okay. Your last reply persuades me that you are not being disingenuous.

“The status quo may not have productivity growth, thus preserving it will not lead to increased productivity. QED.”

Unfortunately QED requires that you don’t make a formal deductive error: from “may” not have growth one can only deduce “may” not lead to increased productivity. QED also requires that you don’t commit the informal fallacy of wrong conclusion: the existence of an exception has little bearing on the likelihood of an outcome.

Let us not forget that my assertion is that the expected result, all else being equal, of adding people to free trade, is an overall increase in productivity, compared to the nontrading state. As a simple illustration, I gave you the case of just two people.

We are, of course, talking about populations of people. So let me try this approach.

You have 1000 experiments each of which is simply as follows: Two people who are currently self-sufficient discover one another. They each are given the choice about whether or not they will trade with each other.

Let’s be clear:

1. The choice is left up to the individuals. We are not assuming any particular choice per se. We are assuming only that they are humans, acting as we expect humans to act.

2. The environments for the individuals may vary in a random or even haphazard way across experiments, but the environment immediately pre- and post-choice within each experiment is unchanged. Only the effects of the choice cause any change.

3. You don’t know the environments in which the experiments are taking place except to the extent the experiments are possible (the individuals have been self sufficient).

Now which of the following do you think is true?
A) It is most likely overall productivity would increase.
B) It is most likely overall productivity would decrease.
C) It is most likely overall productivity would not change.
D) Two or more of the above are equally likely.

“Okay, so if you think people usually choose in their best interests, how can you think the choice to maintain the status quo unless a mutually beneficial alternative exists, does not on the whole lead to increased productivity?”

But here is the simplest way to show that your argument does not follow.

The status quo may not have productivity growth, thus preserving it will not lead to increased productivity. QED.

If you’ll notice, the texture of the discussion thus far has been, you posit a theory, I produce a counter example, you not understand and rinse and repeat.

If you lay out the argument, you’ll see that it requires many assumptions that may or may not hold. This is a perfect example of why modern econ is done rigorously with math and formal proofs. What “sounds true” does not necessarily logically follow.