Vertical & Horizontal Arguments

Since I’ll be spending a lot of time refuting philosophical arguments, it’s useful to make a distinction between two types of arguments. One I will call a vertical argument and the other a horizontal argument. What distinguishes them is their dependency on other parts of the argument, and how easy they are to refute. Let me explain.

Let’s think of the horizontal argument like a chain that is holding up a chandelier hanging from the ceiling. If any link on that chain is weak or breaks, then the chandelier falls. Many an argument is built like that. They are cumulative: each step builds on the previous step. A good example of this would be a mathematical proof, like say Euclid’s proof of the Pythagorean Theorem from Book 1 of the Elements. The argument is built on dozens of steps: a series of definitions, five postulates, forty plus proofs that themselves have several steps to them, and then finally an elaborate argument tying them all together.

Let’s think of the vertical argument like a wall of bricks. The pieces work independently and the more elements, the stronger the argument. For example, an argument in a courtroom. Imagine you’ve got a man you suspect murdered his wife. You have a) a gun at the crime with his fingerprints b) a bullet in her that matches the gun c) a neighbor hearing a gunshot d) someone seeing him drive away shortly after the gunshot and e) an attempt to collect on his wife’s life insurance. Individually, none of these really prove much of anything, but cumulatively you have a pretty airtight case. They don’t depend on each other, so if you knock down one of them, the rest still stand. If you knock down one of them, the overall argument will be weakened but not refuted.

You see, with a horizontal argument, like in the courtroom example, the more individual pieces the stronger the argument. The wall grows stronger and becomes more and more invulnerable even if some holes are poked in it and certain pieces are shown to be fallible. But with a vertical argument the more pieces it has the weaker it is, because it more potentially weak chain links. If you’ve only got three parts to the argument, it’s relatively easy to assure that all three are solid and tempered. But if you’ve got twenty pieces, fallible as we humans are, there’s bound to be a weak step that you’ve included somewhere. This is why it’s a good rule of thumb: the more complex a philosophical argument is the more likely it is to be flawed.

These two aren’t mutually excusive, you could have several vertical arguments supporting a single point, like several chains holding up a chandelier, which gives a much firmer grip, and requires much more to refute.

Vertical argument allow one to construct far more complex ideas, which are more attractive to philosophers and historians of philosophy, and they certainly can be more interesting, but they are more vulnerable and usually represent vast airy spider webs that are swept aside with the wave of a hand.

For my next post I'll look at Anselem's Ontological Argument for God's existence.