## Reasoning and Logic

### Types of Reasoning

Posted on September 26, 2009 by Peter Turney

I was reading the Wikipedia page about Reasoning and the associated Discussion page (by the way, I find the discussion pages are often at least as interesting as the main articles, and sometimes more interesting), and it seems to me that we don’t have a good classification of the various types of reasoning. The page on Logical reasoning describes the three-fold division that is most familiar to me — induction, deduction, and abduction — but the page on Reasoning prefers a two-fold division — induction and deduction. On reflection, neither of these seem adequate to me.

Wikipedia and Stanford Encyclopedia of Philosophy have articles on the following types of reasoning:

The two-fold division of deductive versus inductive really amounts to deductive versus non-deductive, which isn’t fair to the various kinds of non-deductive reasoning.

I guess we should start by defining reasoning. I don’t like the definition on the Reasoningpage:

Reasoning is the cognitive process of looking for reasons for beliefs, conclusions, actions or feelings.

I prefer the following definition, which is a variation of a definition that once appeared on the Inference page:

Reasoning is the process of deriving consequences from premises.

The various types of reasoning mentioned above can all be viewed as algorithms, or broad classes of algorithms, that take premises as input and generate consequences as output.

Deductive reasoning seems to have a special status in this list of types of reasoning, perhaps because deductive reasoning is the foundation of mathematics. There are various logical systems for deductive reasoning, but they all share this defining property: If the premises are true (and consistent, although there is paraconsistent logic) and we follow the rules of the given deductive system (e.g., first-order predicate calculus), then the consequences will also be true. This is a very attractive (seductive, even) property for a system of reasoning. (Although deductive reasoning is vital to math, the problem of interestingness in math is arguably more interesting than the problem of truth.)

Statistical reasoning also has a kind of guarantee: If we know the probabilities of the premises (and these probabilities are consistent) and we follow the rules of the given statistical system, then we can calculate the probabilities of the consequences.

It’s tempting to classify the various types of reasoning according to the kinds of guarantees that we have about them, but I think this is the wrong path to take. In deductive reasoning, how do we know that the premises are true? In statistical reasoning, how do we know what probabilities to assign to the premises? These questions lead to endless debate, but the ultimate answer is that we don’t know. This limits the value of these guarantees.

I prefer to take an evolutionary perspective on knowledge. We don’t know anything for certain; everything is open to doubt, but incremental doubt: doubt one thing at a time. We can even doubt the (standard, traditional) rules of deductive reasoning, such as the law of the excluded middle.

From an evolutionary perspective, the various kinds of reasoning listed above are like species of animals that have evolved over time. It might be fruitful to look at the evolutionary tree for these species of reasoning, just as cladistics is useful for biology. From this perspective, it is interesting that both deductive reasoning and analogical reasoning can be traced back to Aristotle.