How to Reason Using Good Logic

Being logical helps us deepen our relationship with God and so helps us become better Catholics.

Our relationship with God is like our personal relationships: the more we know God and others, the better we can interact with them. God wants us to know Him by having Faith in His Revelation. Understanding Faith to any degree requires the use of logic, which takes its most refined form in Orthodox Theology. God also wants us to know Him through Reason, which is the use of non-supernatural evidence and logic. The most refined form of Reason is true Philosophy.

God wants us to know Him so that we can interact with Him the way He wants us to interact with Him. Applying Faith to our lives requires the use of logic. For example, real conscience is an exercise in logic—“a judgment of reason,” as the Catechism (1778) calls it—and it is not an emotion, an intuition, or some other goofy thing it has been misconstrued to be in the last sixty years of so much abysmal religious education, preaching, and spiritual direction.

Pope Francis, for example, used logic in his “Letter to the Bishops of the Whole World” which accompanied his recent motu proprio (Traditionis Custodes) on the Traditional Latin Mass (i.e., the Mass that uses the Roman Missal promulgated by St. Pius V and edited by St. John XXIII in 1962, also known as the Extraordinary Form of the Mass).

Logic is a natural ability for human beings. Humans have always “added 2 and 2 together.” Whenever human beings have been intelligent, they have used logic. Unlike animals who get by only on stimulus-response, instinct, and memory, we human beings must use logic—whether making a purchase, doing a job, or spending our leisure time. We cannot not use logic. The only question is whether we will use logic well or poorly, including in our efforts to know God and do His Will. Like any other natural ability, logic is done better when it is understood better.

Argument and Proposition

At its most basic, logic is having reasons for what we think and say, which is why a synonym for logic is reasoning. Logic is expressed in an argument, which is a group of statements (assertions or claims) such that one or more statements are reasons for (cause, support, or lead to) another statement. So argument has a different meaning in logic than it does in an everyday conversation where it means “disagreeing” or “quarreling.” Here is one of the arguments (Example #1) made by Pope Francis in his “Letter”:

Because the opportunities for wider use of the Traditional Latin Mass offered by St. John Paul II and by Benedict XVI have been exploited to significantly wound the unity of the Church, and because significant wounds to the unity of the Church should not be tolerated, therefore this new motu proprio is needed to supersede all previous Vatican instructions and permissions regarding the Traditional Latin Mass.

In logic, the term for a statement is a proposition. Propositions can be expressed as clauses in one sentence or as separate sentences. In Example #1, the first two propositions (“the opportunities for wider use . . .” and “significant wounds . . .”) support the last proposition (“this new motu proprio is needed . . .”).

Conclusion and Premise

Every argument is made up of two kinds of propositions. The proposition in an argument that is supported by (follows from, results from, or is caused by) the other proposition is the conclusion, which literally means “to close with.” Every argument always has only one conclusion. In our example above, the conclusion is the last proposition. The words, therefore, thus, so, hence, and consequently signal conclusions.

A proposition in an argument that supports (causes or is the reason for) the conclusion—a proposition from which the conclusion follows (or results)—is a premise, which literally means “to send before.” In our example above, the first two propositions are the premises. The words because, since, for, for the reason that, as, and inasmuch as signal premises.

Real conscience, by the way, uses Catholic doctrine for its premises. It does not use values or principles that contradict Catholic doctrine. It never comes to a conclusion that contradicts Catholic doctrine.

There is no particular order or format in which premises and conclusion must be expressed. I have formatted examples in this column only to make my points clearer. The conclusion can appear anywhere in an argument. What makes for an argument is the relationship between the propositions. The following example (Example #2) is just as logical as Example #1:

This new motu proprio supersedes all previous Vatican instructions and permissions regarding the Traditional Latin Mass. The opportunities for wider use of the Traditional Latin Mass offered by St. John Paul II and by Benedict XVI have been exploited to significantly wound the unity of the Church. Such division should not be tolerated.

The phrase draws a conclusion provides insight into the nature of logic or argument. Draw in this context means “pull,” not “sketch.” So an argument is a group of propositions such that one proposition (the conclusion) is pulled from or pulled out of the other propositions (the premises).

Valid Arguments and Fallacies

When it comes to trying to be logical, there are two kinds of arguments: valid arguments, which succeed at being logical because their premises DO support their conclusions, and fallacies (invalid arguments), which fail at being logical because their premises do NOT support their conclusions. A fallacy is bad logic; a valid argument is good logic.

Consider Example #3:

Because Pope Francis has the charism of infallibility,

therefore his new motu proprio is infallible.

Example #3 is a fallacy. Its premise (“Pope Francis has . . .”) fails to support its conclusion (“his new . . .”) because it misunderstands infallibility. (Infallibility does not extend to disciplinary measures such as this motu proprio.) Example #1, like its restatement as Example #2, is a valid argument. Pope Francis is being logical, however . . .

Sound Arguments and Unsound Arguments

When it comes to truth, there are two kinds of valid arguments: sound arguments, in which every proposition is true, and unsound arguments, which have at least one false proposition anywhere in the argument (either a premise or the conclusion).

Consider Example #4:

Because every pope has been a socialist, and

because Donald Trump is the pope,

therefore Donald Trump is a socialist.

Although every proposition in Example #4 is ridiculously false, it IS a valid argument. It is perfectly good logic because its premises DO support its conclusion, which is all that is needed in order to have a valid argument. It is NOT a fallacy; it is an unsound argument.

It should give us pause that an argument does not need to have true propositions in order to be valid, that false premises can support a false conclusion, that human beings can be perfectly reasonable and yet be thinking or telling falsehoods. Someone can be perfectly logical and yet be out of touch with reality. Someone can be intelligent (logical) and yet not be knowledgeable or wise. For a brilliant elaboration of this, see “The Maniac,” Chapter II of G. K. Chesterton’s Orthodoxy.

I submit that Pope Francis’ argument in Example #1 is unsound. Its conclusion (“this new motu proprio is needed . . .”) is false because its first premise (“the opportunities for wider use of the Traditional Latin Mass . . . have been exploited to significantly wound the unity of the Church”) is false. Infallibility also does not extend to assessing the current state of the Church—it only extends to certain doctrines.

Inductive Arguments and Deductive Arguments

Valid logic can be stronger or weaker. When it comes to the strength or weakness of logic, there are two kinds of valid arguments.

A deductive argument is an argument in which the conclusion must follow from the premises. If the premises were true (whether or not they really are), then the conclusion would have to be true, as in Example #4. The conclusion in a deductive argument follows necessarily from the premises. Pope Francis’ argument in Example #1 is deductive.

An inductive argument is an argument in which the premises offer some support for the conclusion. If the premises were true (whether or not they really are), then the conclusion could still be false. An inductive argument with true premises can have a conclusion that is true, and an inductive argument with true premises can have a conclusion that is false.

There are two different kinds of inductive arguments: weak inductive arguments that only give possible conclusions and strong inductive arguments that give probable conclusions. The conclusion in a weak inductive argument possibly follows its premises, and the conclusion in a strong inductive argument probably follows its premises. The less possible the conclusion, the weaker the argument; the more probable the conclusion, the stronger the argument.

Another argument, paraphrased, made by Pope Francis in his “Letter” (Example #5) is:

Because a questionnaire about the Traditional Latin Mass which I (the pope) sent to the bishops shows that the Traditional Latin Mass now significantly wounds the unity of the Church,

therefore I need to issue this new motu proprio.

This argument strikes me as being a very weak inductive argument. It assumes that those bishops who think negatively about those who worship at the Traditional Latin Mass actually know well those who worship at the Traditional Latin Mass. Although I prefer to worship in the Ordinary Form of the Mass, I know many good Catholics who prefer the Traditional Latin Mass and who are terribly misrepresented in Pope Francis’ “Letter.”

No deductive argument is stronger or weaker than any other deductive argument since deduction is already the strongest possible logic. Inductive arguments can be made stronger by adding more premises to support the conclusion. It can be difficult to distinguish between extremely weak inductive arguments and fallacies.

Sound arguments can be both deductive and inductive. Unsound arguments can be both deductive and inductive.

In Conclusion

We need to be aware of the premises that support conclusions, which every pre-school child prods us to do by incessantly asking us, “Why?” “Why” is the natural short-hand way of asking, “What are your premises?” We also need to know whether premises support conclusions validly or fallaciously. Even better, we need to know if a conclusion follows its premises necessarily, probably, or only possibly. Best of all, we need to know whether all the propositions in an argument are true so that we do not confuse unsound arguments with sound arguments and be led by good logic into falsehood.

Every high school student should know these distinctions which make for clear thinking. Furthermore, high school students should learn the classic fallacies and the classic valid forms which function as such regardless of the content of the propositions in them. From my own experience teaching high school, I have seen that they can.

The best of all arguments is the sound deductive argument since it combines truth with a necessary conclusion. I finish with a deductive argument which I claim is sound:

Because those priests, bishops, and leaders of Catholic institutions who dissent from doctrine are a far more serious wound to Church unity than the Traditional Latin Mass as it was being celebrated according to previous Vatican instructions and permissions, and

because the pope should serve the unity of the Church,

therefore the pope would better serve the unity of the Church by correcting those priests, bishops, and leaders of Catholic institutions who dissent from doctrine than by issuing his new motu proprio.

For more insight into Pope Francis’ motu proprio, I strongly recommend columns written by Cardinal Gerhard Mueller and Father Gerald E. Murray.

P.S. Has Pope Francis “weaponized” the Eucharist against those who prefer to worship at the Traditional Latin Mass?