Modus Ponens, Logic and the Word of God

Modus Ponens names a particular law of logic, said to be "formal." Formal logics differ from informal in the following manner. In formal logics, the "form" of the argument renders it valid, not the particular content plugged into the place of the variables. With informal logic, the particular content of propositions makes an important difference. Here, the fallacies [the rules for reasoning poorly] bear a particular form, not the rules for reasoning correctly.

A valid argument has conclusions which necessarily ensue from its premisses (this is the old spelling; the newer - incorrect but popular - is "premises"), regardless of whether the premisses prove true or false. Put differently, this means that validity concerns itself only with reasoning in straight lines, so that the truth-status of the premisses transfers to the conclusions through a necessary chain. One can never deduce more for the conclusions than is already present in the premisses (by implication) from a valid argument.

An argument with only false premisses, must (in order to be a valid argument) have only false conclusions. Likewise, for true propositions and their corresponding conclusions. If the premisses are mixed -- one or more is true, AND one or more false, then certain combinations, and only those, are possible with valid arguments. This is what "truth tables" demonstrate.

Now MP represents a formally valid argument, regardless of the content used. To get a sound argument, not merely a valid one (which we must, from biblical necesssity), one must employ a valid argument, and then use only true premisses for it. These two conditions entail "only true" conclusions.

Now MP is a very basic (simple, not complex or compound) law of logic, which takes the form of: "If P is true, then Q is true; P is the case; therefore, Q is the case. Sometimes propositions spell out causal relationships (where P is the physical cause of Q) and sometimes, it spells out only intent. I will not go into this at length, but suffice it to say there are different KINDS of applications for MP.

For example, here is the MP of intentionality.

If it is tuesday, I will go to work.
It is tuesday. Therefore, I will go to work today.

Here, the two parts of the conditional clause (most any "if-then" statement is called a "conditional," or a "conditional clause") are linked together to specify a man's typical habit. He goes to work on Tuesdays. Now did this man actually GO to work on the tuesday this affirmation was spoken or written? We don't know. Even if he did not, the argument would still be valid. We only know that he says he INTENDS to go to work if it is tuesday.

This may not even refer to any actual person, but specifies only hypothetical circumstances. It is still valid as an argument, for, given the truth of the premisses, the conclusion must follow.

So then, logic textbooks do not specialize -- you will have gathered from this brief excerpt -- in supplying a list of true premisses. When the do, the list turns out in most every instance either challengable, or else simply erroneous. Here is a typical syllogism, affirming Modus ponens, applied to sets and members.

All men are mortal.
John is a man.
Therefore, John is mortal.

This can be rewritten to illustrate modus ponens, as:

All men are mortal.
If John is a man, then he is mortal.
John is a man. Therefore, John is mortal.

Question -- Is it true that all men are mortal? Of course not. Jesus is a man, and he is immortal. So, not all men are mortal. This also implies knowing that John is a man does not necessarily imply that he is mortal (since this does not work in the case noted above, and many saints in heaven bear the name John -- i.e. Chrysostom, Calvin, Knox, etc).

The term mortal needs defining as well. If this means "one who can die," then all the host of heaven (who have already died, but are quite alive) -- would not qualify. In other words, John (if it refers to John the Baptist) would be false in one sense. The precise defininition of words like "mortal" and "death" as well would need to be known in advance to certify whether or not the premisses are true.

If you suppose this would require a much larger context -- a broader semantic field or network of beliefs - of propositions already known to be true - in order to verify or falsify any particular one claim, then you have hit the proverbial nail on the head. This is why logicians are so squeamish about supplying a list of "true propositions" to start with. They know all too well that one might challenge any claim whatsoever, even laws of logic. And many have.

Do classroom logicians typically stand ready to defend a particular and well-defined worldview (semantic web)? Not on your mortal life. Thus are Christians uniquely suited to the logical task, already possessing (as we do) a coherent worldview found in the canon of Holy Scripture, which provides a list of true propositions, each of which assumes the truth of the others in its own affirmation.

In other words, laws of logic, like Modus Ponens, need the Bible in order to make sense of a truth claim pressed into the variables (usually P and Q)used to illustrate it. Mind your P's and Q's.

How do logicians then teach anything? They often teach the truths of validity without affirming their application (other than hypothetically)in any one instance, or else they use tautological instances no one would care to challenge, since they are true by definition, without pointing to new information in the world outside the classroom.

Here is your trivial example. If dictionaries are opened, they display words.
Dictionaries are opened. Therefore, they disply words right now.

This argument is both valid and utterly worthless. It could be sound and worthless too. But MP can be used in combinations with other laws of logic to construct powerful tools for use in reasoning -- in very controversial ways (my favorite) -- to apply the Holy Scripture to other propositions found in the Word (to learn more from the Bible) or applied to the world around us, to learn more about science and the world (and of general revelation too).

So MP by itself may not seem so impressive. But in valid combination with other laws of logic (and their implicates), it can be used with great effect to the Glory of God.

To be sure, various challenges to MP have availed themselves of philosophers from time to time, and I cannot now rehearse them for time's sake. But suffice it to say, that when one challenges a law of logic (as with MP) his argments in every case will end up either presupposing its veracity, or else implying it. This is the nature of transcendental truths. Their prosecutors undermine their own case.

But when we think about Modus Ponens, we must also remember that true propositions come only KNOWABLY from the Word of God, or from ways of knowing which the Word warrants. For instance, the Bible says, "The eye that sees and the ear that hears, the Lord has made them both." The Bible also says that God made all things very good (sufficient to their intended purpose).

When you combine these propositions, you end up with the conclusion that your senses are generally reliable. If your eyes tell you that your lawn is green, you have the right and duty to assume that this is true unless and until you have countervailing evidence. You might be wrong. It happens now and again. But the reliablity of your senses is warranted by Scripture. Augustine noted that any attempt to get by with the opposite assumption (for any extended period) would be extremely hazardous.

This was his way of noting the transcendental nature of the reliablity of your senses. Any argument for or against their general reliability will necessarily assume that general reliability. This makes the proposition, "Your senses are generally reliable" logically necessary, and mandatory for practical purposes. It must be true for you to know anything.

Deaf people know they are deaf. This is because their other senses are still generally reliable. There are exceptions - drugged out people sometimes do not have reliable senses; sometimes drunk (or badly dehydrated) people have the same problem. The exceptions prove the rule of general reliablity -- which is not the same as indestructible infallibility.

In any event, the difficulty professors often have of supplying true propositions (which philosophers have not attacked with some success) for illustrating non-hypotheical uses of Modus Ponens, teaches us something important about logic courses. It shows how necessary it is to presuppose "canonical soundness" in order to make sense of the idea of logical validity, and in applying logic to the real world.

Changing the subject slightly, we should not that a "causal use" of MP highlights the "antecedent" (that is what they call P) as the cause of Q (the "consequent,") so that Q follows both from physical necessity -- when you drop an apple it necessarily falls -- and from logical necessity too. For an example combining these two ideas, we turn to the topic of cars and keys:

If you turn the key, the ignition system will start the car.
I did turn the key. Therefore, the ignition system started the car.

Now, sometimes P and Q are not related in any way other meaningful way, other than by the fact that they both happen to be filling in the blanks of the same illustration. This always seems weird so professors like teaching it.

If the moon is blue on monday, then cheese will fly.
The moon was blue last monday. Therefore, the cheese was flying.

Rendered as silly as one might make it, this argument still maintains a valid posture because the form follows the modus ponens recipe. Laws of logic do not pay much attention to particular content, but only seek to match truth-values of premisses and conclusions, and manage a logically necessary link between them.

Besides the fact, that MP is a "law" of logic, the fact that its conclusions follow from necessity (because of the argument's FORM) shows that this is actually an aspect of general revelation. Laws are universal, and so is necessity. A contingent truth is true because of historical details, and a necessary truth because of general rules (laws).

This is why MP has a transcendental character (whether you argue for it, or else against it, you will either employ or imply it). Nature's light is not optional, but necessary, since it is inescapable. And one cannot escape it for (primarily) two reasons: 1. God is sovereign (which implies that when he seeks to reveal Himself to ALL men, he cannot fail) and 2. God created a world endowed with wisdom universally (down to the very atomic structures of all things, and at even smaller levels).

If they ever do actually find the subatomic limits of the smallest particle, they will I am sure, encounter a very very tiny sign, which reads, "God is wise and you are not." This wisdom -- structural wisdom and wise integration of all things interacting together -- is necessarily universal.

These two features of the Cosmos -- a wise and soverign Creator as Lord of it, and the universal wisdom with which he endowed his creation -- give rise to MP and the other laws of logic. Logicians can run [classrooms], but they cannot hide. Like everyone else, they must use logic - including MP - to get by and do ordinary sorts of things. They do in fact "plug in" real content into the P's and Q's in their unguarded moments.

This is where Christian logic (logic that CAN actually have knowably true content for use in class), and Christian apologetics, begin. The beginning of logic is the fear of the Lord. For logic is a necessary aspect of Wisdom (one cannot be wise without the use of logic, whether he studies it formally or no). Wisdom is more than mere logic, but it is never less. And those who do not fear the Lord severely limit their ability to teach logic, for the Word of God is the foundation of it.

So let us finish with a MP syllogism of our own.

If the Word of God is the foundation of logic, logic studies will proceed badly without it.

The Word of God is the foundation of logic; therefore, the study of logic proceeds badly without it. How does it proceed badly?

1. Logicians often end up challenging real laws of logic (since they have no canonical limits to tell them which proposed laws of logic really are or are not actual ones).

2. Logicians widely dissent from each other as to just what counts as truthful and useful information one might use to illustrate laws of logic in class, to guarantee not only valid arguments, but sound ones. Christians, who are commanded to be sound in the faith, do not have the luxury of this nearly total indeterminism, regarding true claims. It's really quite funny that logicians, who are supposed to be so wise, have almost no "true proposition" content to offer, which they are willing to defend in class.

3. Logicians often use - in both informal and formal logic texts - examples which turn out to be false, and which can be so demonstrated using their own lesson plans. The classic "bogus example" comes from informal logic texts regarding circular reasoning. They habitually use the citation of 2 Tim. 3:16, used as an example to prove the truthfulness of Scripture, to illustrate this fallacy.

This is in fact, exactly the biblical pattern since, as the highest standard, any appeal to some other standard for proof would imply the denial of just what we seek to prove. This is the case with the final standard of proof in EVERY belief system, Christian, religious or secular -- of any kind whatsoever.

The buck has to stop somewhere. And that final highest appeal if asked for proof of its accuracy will have to cite the final standard chosen FOR THE PROOF. This highlights the necessary and NON-FALLACIOUS nature of cirularity at the level of highest, or finally authoritative standards.

Not all circles are of the same kind. The biblical version CAN provide a coherent account of why things appear as the do, of the preconditions for logic, science and morality, while the other circles cannot. Only at lower levels (not final ones) of authority, does one properly cite circular reasoning as a fallacy.

This was implied by Bertrand Russell's set theoretical development of "meta-classes." But that is another story.

The bottom line is this: If one stubbornly insists that ALL forms of circular reasoning are of the same kind (which is simply counterintutive since examples to the contrary are not hard to show), then he implies that all worldviews are inherently fallacious -- since they all appeal to their highest standard by that standard (or else ARBITRARILY dismiss dissenters out of hand). If they appeal to some other standard, then that one, not the first, is in fact the highest standard. An infinite chain of justifying standards -- which are therefore not justifying at all - follows upon the denial of this claim.

This implies that no knowledge obtains. If it is ultimately arbitrary, it is not justified, and if not justified, it is not knowledge. But no law of logic is properly formulated apart from the whole canon of Scripture, as a system of knowledge, informing that law, in regard to its proper content (what should we assume when reasoning?), its nature (what is a law of logic?), its scope (how broadly does it apply?) and its limits (what is a wrong application of it, and how do you know?).

The Bible has the answer, and biblically-illiterate logicians do not. From the divine viewpoint, they combine logics with ebonics, frustrated in their efforts by unbelief. This means the only rational course of action would be to stop thinking in ways destined to make logic impossible. In Christ are hid all the treasures of wisdom and knowledge. This means that Christ holds the key to understanding logic properly and accurately -- from its basics to its most technical and formal expressions, as he is offered to us in all the Word of God.

If any lacks wisdom, let Him ask of God, who giveth liberally without finding fault. And study up.