## The rules of right reason

It is doubtful that there is a set of rules that can properly be called “the rules of right reason.”  However, this issue has resurfaced at Uncommon Descent (an ID blog).  The issue last arose the a little over a year ago, when Barry Arrington banned many commenters because he saw them as violating the rules of right reason.  There’s good discussion of that event in a post at The Skeptical Zone.

The issue resurfaced in a recent post at UD, when Barry Arrington questioned whether Kantian Naturalist was reasoning rightly.  Then kairosfocus, another contributor to the UD blog, added his support to the view expressed by Barry Arrington.  His post begins with:

In our day, it is common to see the so-called Laws of Thought or First Principles of Right Reason challenged or dismissed. As a rule, design thinkers strongly tend to reject this common trend, including when it is claimed to be anchored in quantum theory.

Going beyond, here at UD it is common to see design thinkers saying that rejection of the laws of thought is tantamount to rejection of rationality, and is a key source of endless going in evasive rhetorical circles and refusal to come to grips with the most patent facts; often bogging down attempted discussions of ID issues.

Presumably kairosfocus, and perhaps many other ID proponents, see something irrational about a refusal to accept these so-called rules of right reason.

So what are these rules?  Barry Arrington expresses them this way:

For any proposition A:

1: A=A. True or False.

2: “A is B” and “A is not B” are mutually exclusive. True or False.

3: “A is B” and “A is not B” are jointly exhaustive. True or False.

These are the rules of classical propositional logic, and are widely accepted as such, even by those whom Barry Arrington and kairosfocus would criticize.

The third of those rules is often called “the law of the excluded middle”.  It is now around 100 years since L.E.J Brouwer founded his school of intuitionist mathematics, and Brouwer dissented from the law of the excluded middle.  So objection to the stated rules is not a new fad.

The thing to notice about those rules, is that they are rules of abstract logic.  Most disagreements are not about logic, but about how to apply it in the real world.

### Dichotomies

Before we can use these rules in the world, we must find a way of expressing things in propositions.  Here’s how kairosfocus says that we take that step:

In short, to think reasonably about the world, we must mentally dichotomise, and once that is done, the first principles of right reason apply.

That step of dichotomizing is not part of the stated rules of right reason.  It is outside those rules.  And the dichotomizing is a prerequisite to being able to apply the rules.

The disagreements are more often disagreements about dichotomizing than they are about the stated rules.

### An example from automata theory

This semester, I am teaching a class introducing students to the theory of computation.  At present we are just beginning the discussion of Turing machines.

It is common to express the theory in terms of languages.  We take a word (a string of letters from a finite alphabet), place it on the input tape of a Turing Machine, and see whether that TM accepts the word.  The set of words that are accepted can be considered a language.

We began the class with finite automata and the regular languages that they define (usually called regular languages).  Given a finite automaton, and a word, the FA either accepts the word or rejects the word.  So there’s that kind of dichotomy that kairosfocus wants to use.

Next, we moved on to pushdown automata, and their languages (context free languages).  With a pushdown automaton (or PDA), a word is either accepted or rejected by the automaton.  So, again, we have that dichotomy.

But once we get to the Turing machine, things become more complex.  Some words are accepted.  Some words are rejected, and some words are neither accepted nor rejected (the TM just keeps going forever, and never makes a decision).  So there is no easy dichotomy.  And, to make matters worse, there is no general way of identifying which words are neither accepted nor rejected.  That’s the halting problem, which has been proved unsolvable.

So there’s the problem for Barry Arrington and kairosfocus.  There insistence on simple dichotomies does not fit the world.

### Finitism

It is, of course, possible to insist that our world is finite, so that there are no actual Turing machines.  And it is possible to ignore quantum mechanics (another area where simple dichotomies do not work).  In such a finitistic non-quantum world, one could assume clear dichotomies.

The trouble with this, for ID proponents, is that they also like to appeal to Gödel’s incompleteness theorem, and Gödel’s result is pretty much equivalent to the halting problem.

$1 + e^{i\pi} = 0$