Why Fallacies are False -- the Math

Fallacies are errors in logic. Logic is not “a wreath of pretty flowers that smells bad.” Nor is it wordplay.

Logic connects up with two fields of mathematics and I’m going to use both of them so settle back.

Symbolic logic is one way of representing set theory in math. You define a set of elements (which may have nothing in it) and then you can do actual math: add, subtract, multiply, and so on. One part of this field is the stratospheric issue of infinite sets, some of which are bigger than others. If that blows your mind, dig around and find work on it.

You can say things with set theory that are not even wrong but you can also estimate the probability that you are right. I have used probability calculations and identification of fallacies to argue against Documentary Hypothesis, which I first heard about in the 1970s from one of my favorite science authors. I also used the Test of Occam’s Razor, which DH fails in many ways.  I have about 50 posts with the details.

http://pajheil.blogspot.com/2017/07/fact-checking-torah-structure-of-torah.html

When you talk fallacies, you also have to talk formal epistemology. How do we know what we know? What sources of data do we use to get elements for our sets? This is the hill on which so many conspiracy theories die. They fail the Test of Occam’s Razor because they don’t address all the available data, or they use sources that misrepresent the data. Conspiracy theories and DH have this in common.

By the way, the other way of representing set theory is Venn diagrams, those colored circles that intersect or not. Gary Curtis has some Venn diagrams on his site. Here’s an example.

https://www.fallacyfiles.org/somernot.html

The math shows that logic is not just wordplay. It’s also an example of why some mathematicians say, we don’t invent math, we discover it. The oldest description of logic that we know of is in Aristotle’s Organon, comprising his Categories, On Interpretation, Prior and Posterior Analytics, Topics, and On Sophistical Refutations. You can find these works free online and can download them for free.

https://archive.org/details/AristotleOrganon

But probability math is rooted in gambling and the first calculations come from the 1600s CE, while set theory is the work of the late 1800s CE and in that century, Venn adapted Euler diagrams to help with studies of Boolean logic.

As with any good STEM field, it all fits together around the edges – and it helps show objectively why a fallacy is wrong.