• Kenneth Jacobs

The Rules of Reasoning We Follow

Updated: Jan 26

Inquiry comes in many forms; not just in science, but in civilian life too.

Scientists and civilians observe phenomena, manipulate phenomena, and develop propositions about those phenomena. There are many ways to observe and to manipulate our subject matters of interest, but there are only so many ways to form a judgement about them. The rules of reason we are taught––implicitly and/or explicitly––constrain the judgements we put forward.

The rules of reason we follow are known as:

  • Deduction

  • Induction

  • Abduction or Retroduction

These are our "-ductions", the rules of reason that constrain us for better or for worse. Let's take each -duction in turn.

Deduction is when we say: “If the time it takes to get to Philadelphia from Boston is 1 hour & 30 minutes as the crow flies, then we can expect to be there in about 6 hours drive-time.” Deduction is said to be an argument from the general (as the crow flies) to the specific (6 hours given the actual twists and turns). In the current deduction our ETA is a prediction made with limited information. Absent any GPS device, and left with only flight-time and terrestrial know-how, we can make a relatively specific and somewhat accurate prediction about expected drive-time. This is our deductive reasoning in action; it is our ability to use some base information to infer a specific circumstance or outcome.

In the case of induction, we do the inverse. Rather than argue from general-to-specific, we argue from specific-to-general. Induction is when we say: "If they've got a New Jersey license plate, then watch out! I've been cut-off by them more than once." The induction involves the derivation of a general rule based on the limited experience one has with New Jerseyans driving. We reason that if one New Jerseyan is bad at driving, then they must all be bad at driving. Note that we have in no way accounted for their driving skills; we've only attributed "bad driving" to a population of individuals defined by geographical region. Our induction at this point is mostly erroneous, meaning that our general rule about New Jersey drivers probably doesn't hold true under all circumstances. For our general rule to hold water, it must be qualified. For example, New Jerseyan's are bad drivers when in adjacent states, and therefore, on unfamiliar roads. Our qualification is admission that our general rule is subject to violation.

Abduction or retroduction is when we argue from effect to cause. It is the more common of the -ductions because we use it in our everyday discourse: when we we gossip and form rumors. I'll use the term retroduction from here on out because -retro signals our backward directed action (i.e., thinking from effect observed to probable cause). C.S. Peirce gives an example of retroduction regarding the characters of a man thought to be a Catholic priest. The retroduction is the guess-work involved in determining the status of this man's priestliness.

Peirce described his reasoning:

"I might say to myself, let me think of some other character that belongs to Catholic priests, besides those that I have remarked in this man, a character which I can ascertain whether he possesses or not. All Catholic priests are more or less familiar with Latin pronounced in the Italian manner. If, then, this man is a Catholic priest, and I make some remark in Latin which a person not accustomed to the Italian pronunciation would not at once understand, and I pronounce it in that way, then if that man is a Catholic priest he will be so surprised that he cannot but betray his understanding of it. I make such a remark; and I notice that he does understand" (p. 152-153).

Peirce went on to question how much weight (or confidence) he could attach to that test because it is only a sampling of the many characteristics of a Catholic priest. The guess-work required for choosing a character to test is what makes Peirce's reasoning retroductive. He begins with the observation of a man––the observed effect––and works through the probable causes that may deem that man a Catholic priest. Here is how Peirce described retroductive reasoning:

"The first starting of a hypothesis and the entertaining of it, whether as a simple interrogation or with any degree of confidence, is an inferential step which I propose to call abduction [or retroduction]" (p. 151).

Peirce admits that he cannot attach too much weight to his initial test of the man's priestliness, but his guess-work is "the first starting of a hypothesis and the entertaining of it", so with some "degree of confidence" he can take "an inferential step" toward believing that the man is a Catholic priest. In Peirce's words again:

"It must be acknowledged that it is but a weak confirmation, and all the more so, because it is quite uncertain how much weight should be attached to it. Nevertheless, it does and ought to incline me to believe that the man is a Catholic priest" (p. 153).

What Peirce has reasoned is what we so often do in our daily lives. We observe outcomes such as a car accident and take an inferential step toward learning its cause through retroduction. We can imagine what had happened and where things went wrong for whatever reasons. We can't be sure of how much weight to attach to any potential thought experiment, but we can work out, with some degree of confidence, a likely cause.

Since we so often observe outcomes devoid of their development, we often rely on the abductive/retroductive rules of reason to make sense of the everyday world. In science, retroductive reasoning appears to be most closely associated with inverse problems. An inverse problem is when, for example, a seismologist must reason from an earthquake (observed effect) to its causal factors. The weight attached to any potential, causal factors will inform the seismologist's prediction of future earthquakes.

The rules of reason we follow are imperfect. They are susceptible to misuse and erroneous conclusions. Worldly things change; they develop, evolve, learn, etc. Therefore, the template that is these rules of reason have no preexisting phenomena on which to exactly fit. Even the descriptions of the rules of reason herein are imperfect, as the respective examples for each cannot avoid caveat and overlap with the other rules of reason. At the very least, though, we can be familiar with these often implicit and overlapping rules of reason so as not to dupe ourselves and others.