The following is in no way intended to be an exhaustive treatment of the subject of the syllogism. (Get Brother Francis’ Logic Course for that.) It is a lopsided little introduction, being comprised of two excerpts from “It’s All or Nothing,” an apologetics article I penned a while back. The subheadings are as they appear in that article.
St. Paul wrote, in Romans 3:23, “For all [humans] have sinned and do need the glory of God” (Douay Rheims Version – DRV. The King James Version [KJV] is the same until “…and come short of the glory of God.”) This statement appears to be a universal affirmative. It affirms that every human has sinned. (In context, it divides humanity into two categories: Jews and Gentiles. All these – Jews and Gentiles – have sinned.) If we were to exercise formal logic, the Protestant position would be spelled out in the following syllogism:
- All humans have sinned.
- Mary is a human.
- Therefore, Mary has sinned.
This would be a valid syllogism, according to the rules of formal logic, if the terms used were completely unambiguous. However, if the first sentence (the major premise) admits of some kind of exception, then the syllogism is no help in establishing truth. In other words, if “all” is not really “all,” then the syllogism is useless since, for validity, at least one proposition of a syllogism has to be universal.
It is certain that that same chapter of Romans (Chapter three) contains another apparently universal proposition that is contradictory of Biblical truth, if understood as having no exceptions: “There is none that seeketh after God” (Rom. 3:11). St. Paul is quoting King David’s Psalm 13 (14, in KJV). If the passage is literally true, then no men seek God. However, elsewhere St. Paul says that we were made to seek God (Acts 17:27). And David himself says, “In the days of my trouble I sought God” (Ps. 76: 3). [The KJV has: “In the day of my trouble I sought the Lord” (Ps. 76: 2).] So, here, King David is an exception to his own rule. And this Psalm-with-exceptions is found in the very same chapter of Romans cited as an objection to Our Lady’s sinlessness.
There are sections of Holy Scripture in which, literally to understand “all” as “all” would lead one to an absurdity. Take, for instance, this passage from First Corinthians (9:22): “I became all things to all men, that I might save all.” (The KJV has: “I am made all things to all men, that I might by all means save some.”) Were we to put this passage through the same logical rigors, we would come up with a virtual infinity of absurdities. Witness:
- St. Paul became all things to all men.
- A sword is a thing.
- St. Paul became a sword to all men.
- St. Paul became a sword to all men.
- Eroll Flynn was a man.
- St. Paul became a sword to Eroll Flynn.
The above is known in logic as a polysyllogism (two or more syllogisms stuck together). This is a validpolysyllogism if the term “all” really means “all” in the literal, universal sense, each time it appears in the initial major premise. However, as the final conclusion is an absurdity, the word “all” cannot have that universal meaning.
A Little Logic
Some fairly painless definitions and explanations, which will help in reading this article.
Polysyllogism: An argumentation consisting of two or more syllogisms [see below], logically connected together in such a way that the conclusion of the preceding syllogism becomes the [major] premise of the one following. (Radical Academy)
Proposition: A judgment expressed in a sentence.
Reason: Considered as a power, as the mode of intellectualization in this mortal life; it is the mental process of equating two or more judgments in order to form a conclusion. It is a deliberate power that is engaged whenever we formulate a conclusion or opinion by moving from particular judgments to general ones (induction) or from general judgments to particular ones (deduction).
Syllogism: A structured form of argument wherein a conclusion is drawn from the relation established between two premises. This is done by joining or separating in the conclusion the subject and predicate unequated in the premises.
Another definition: An argumentation in which, from two judgments that contain a common idea and one at least of which is universal, a third judgment, distinct from either of the former, follows with necessity. (Radical Academy)
Note: A syllogism is a process of deductive reasoning (see reason, above). Without getting into the various different kinds of syllogisms, let us say that a syllogism looks like this:
No women are priests. (Major Premise)
Ann is a woman. (Minor Premise)
Ann is not a priest. (Conclusion)
Universal Propositions: Propositions [see above] in which the subject is a universal term used distributively to each and all of the class. (Radical Academy)
Note: These propositions can be in the form of a universal affirmative (e.g., “All farmers are strong”) or a universal negative (“No priests are female”).