Logical Implications


If we were in the fourth century and I told you that the Earth was flat, a reasonable question you could ask me would be, “If you just continued moving in one direction, would you just eventually fall off?”

Now, that wasn’t what I said at the beginning. I simply said the Earth was flat. However, the logical implication of a flat Earth means that there is an edge to it (unless, of course, it is infinite). Apart from the infinity loophole, there is no other way out of this option. Either the Earth is infinitely flat or it has an edge.

Suppose you want to test my question because you are sure you are correct. You say, “Alright, we will continue moving in one direction, and we’ll eventually arrive at the edge, proving what I say is true.” From there, the we begin our journey. Assuming we can somehow move in exactly one direction without being obstructed, we would eventually return where you left on. Therefore, this would invalidate my hypothesis. The Earth could not be flat, or else we would have detected an edge.

So that means it’s flat, right?

Well, not so fast.

An astute observer could say that the Earth is a cylindrical shape, and you and I simply walked along the lateral face of the cylinder. However, barring this cylindrical Earth scenario, the Earth must be some sort of solid that one can walk around and arrive back at the same point once again – a sphere.

What I want to illustrate in this example is that one can get into some pretty interesting scenarios by taking statements to their logical end. It’s kind of like trying to reconstruct the pathway of a conversation, but in the forward direction. And almost always, the person who first made the statement will be surprised with the direction the conversation or train of thought has taken based off of one simple statement.

This has particularly relevant implications as our world gets more and more global. While issue like climate change, maintaining our environment for future generations, and spreading resources more equitably may seem far off and too abstract for many of us to think about, they are issues that will have profound consequences. Therefore, saying that you care about the environment but initiatives to preserve it will have to be put off for this year due to lack of funds means you are choosing to not allocate resources to an important issue. Perhaps it’s not the most pressing issue to you, but it certainly won’t improve (and has the possibility to be worse) through inaction. Therefore, the logical consequence of one person not doing something today to help the environment (multiplied hundreds of millions of times) results in an environment that does not improve.

More generally, this situation of saying something without thinking of its logical implications happens all the time in the media. Statements are made which may sound alright on their face, but are disastrous if one really thinks them through. It might sound like heresy to raise taxes because it affects you right now, but if the quality of your life (and others in the world) improves in the long term, is it worth accepting?

Climate change. Space and other life in the universe. Genome sequencing and editing. The allocation of resources. These are the difficult questions of our time, and quick responses might not be the answer. At the very least, we should require more thinking about them than we currently do. Our current answers tend to be quickly thought up, and averse to change because it’s not the status quo.

Instead of being the first or the loudest, how about we be the first to think through the logical implications of our actions and words?

Related Posts

The Grit to Push Through

Behind the Equations

Quantities in Context

Black Boxes

The Priority of Education

A Splash of Colour

Outside the Curriculum

Through the Minefield

Visuals in Mathematics

The Necessary Details