Technical Reasoning/Examples of Arguments

In this short lesson I just want to look at two arguments which are stated in natural language. The goal here is to see that logic may have use, not just in completely formal studies like mathematics, but also in somewhat more real-world settings as well.

The Morality of Abortion

Here, I am deliberately picking an argument which is philosophical and carries a lot of emotional charge. I want to make the case that logic is useful in settings that have immediate consequences for a person's life.

My point is not to actually litigate the issue of abortion at all, throughout this course. But I do hope to supply the student with logical tools which help them to use precise logic when thinking about it.

Argument:

To kill any innocent person is wrong.

Aborting a fetus is always to kill an innocent person.

Therefore abortion is always wrong.

Geocentrism

Argument for geocentrism:

The earth seems to be fixed in place, as we do not see it move, nor do we feel it move.

The sun comes up from the horizon, makes an arc through the sky, and then sets at the opposite horizon.

In short, we observe the sun rotate around the earth, and therefore the earth is at the center of the sun's orbit.

Argument against geocentrism:

This is only an appearance, because we are attached to the surface of the earth.

Suppose that the earth spins on an axis, and we spin with it. Also suppose that the sun is fixed in place.

Then our observation of the sun would make it look just as if the sun were moving.

Moreover, we do not see the motion of the earth because we are a part of the motion. Because we move with the earth, the earth appears motionless, relative to ourselves.

Moreover, we do not feel this motion because of the size of the earth. Its radius is so large that the centripetal acceleration which we experience is tiny. Because the acceleration due to gravity is so much greater, this is the motion that dominates our experience.

Therefore, the sun is stationary and the earth merely rotates on an axis.

Again, both of these arguments are over-simplified "toy arguments", like the one regarding abortion above. The point of considering them is to continue to improve them throughout the rest of this course, as a model for how to think rigorously in more general scientific settings.