Logic 101

Recently, I have been thinking about formal deductive logic and how it is presented. The two presenters that have most recently impacted, or more truthfully frustrated, me are Dr. David Kyle Johnson via his lecture series entitled “Big Questions Of Philosophy” in the streaming series called “The Great Courses”, and our own Faust on his post “Logic 101”.

To give credit where credit is due, Faust, and I assume his editors, have put a lot of time and effort into what I would call a classic or textbook presentation. Additionally, my concerns might properly be addressed in a more advanced course.

As a simple matter of fact, Logic is not constrained to a bivalent or 2 value system. One can read about Kleene or Priest Logic in WIKI under “3-valued logic”.

As a corollary, the domain of all logical propositions is much larger than envisaged in the work of the two afore mentioned presenters.

Dr. David Kyle Johnson asks his audience to think of any examples where propositions are not either true or false and states that no one has come up with an example. It should be noted that the audience is largely made up of amateur or freshmen students. It is my experience that coming up with examples that are contrary in nature to the examples at hand can be difficult. (In general I regard this technique as an effort to obfuscate the subject at hand, though I cannot be certain as to Johnson’s intent in this particular case).

In Logic 101 under the section entitled Truth, Faust writes:

"Propositions are either true or false. If we cannot determine whether a declarative sentence is either true or false, then it does not contain a statement, for the purposes of logic. Another way to say this is that, logic presupposes that truth or falsity can be assigned to any proposition – an assignable truth or falsity being part of the definition of a proposition. While indeterminacy may be fascinating to the philosopher, it’s useless to the logician. And while the issue of indeterminacy has been insinuated into the subject of logic, we will not consider it here."

One can assume that the domain of propositions in formal deductive logic should be constrained to bivalent logic as Faust does in the above paragraph. However he expands on that point to state

“While indeterminacy may be fascinating to the philosopher, it’s useless to the logician.”, which is simply false. Note: indeterminacy is frequently a 3-valued logic with the values generally denoted True, False and Other.

It seems that multi-valued or at least three-valued logic creeps into the discussions on the topic of logic.

Examples:

Dr. Johnson proceeds to prove that if God is benevolent, all-powerful and all-knowing then God cannot exist. His argument is based on the assumption that each of these propositions have binary values. It seems clear to me that if God, assuming He exists, is not benevolent he could be either malevolent or other. This would ultimately would make Dr. Johnson’s argument invalid.

Under Argument Forms Faust writes:

“1. Either I am dead or I am alive.

2. I am not dead.

Therefore, I am alive.”

This is an example of simply assuming ones’ state of existence, regarding life and death, is bivalent. A person could be other. If you are not dead you could be either alive or other. In real life cases some people can be resuscitated while unfortunately others cannot.

I mention these cases simply to show how easy it is to assume that propositions are bivalent when in fact they may not be.

Other Examples:

The Literary Arts are full of examples of ethical multi-valued truth propositions.

Computer Data Values. Data sets can have a null value in addition to a specific data type.

Example: It is June 4, 2019. This can be true or it can be some other date (false) or there could be no date at all. (At least this was true back in the 1980s. It may have changed).

False dichotomy:

A common objection to a given argument is that we are being forced to choose between two divergent choices when other options exist. It seems, from the examples of Dr. Johnson’s argument that God does not exist and Faust’s argument about life and death, that there can be multiple options in the truth values as well.

Summation:

I do not object to teaching bivalent logic. It seems to me that there is a class of propositions which do evaluate to two and only two values. (One must be very careful when giving examples). It also provides intellectual discipline, something that may be sorely lacking these days.

However, trying to deny or minimize multi-valued logic simply distorts the world in which we live.

We should consider a more skeptical view of what is classically presented as a bivalent proposition and we should broaden our logical tools to include a multi-valued logic.