I call upon You, Lord, God of Abraham and God of Isaac and God of Jacob and Israel, You who are the Father of our Lord Jesus Christ, the God who, through the abundance of your mercy, was well-pleased towards us so that we may know You, who made heaven and earth, who rules over all, You who are the one and the true God, above whom there is no other God; You who, by our Lord Jesus Christ gave us the gift of the Holy Spirit, give to every one who reads this writing to know You, that You alone are God, to be strengthened in You, and to avoid every heretical and godless and impious teaching.

St Irenaeus of Lyons, Against the Heresies 3:6:4

Thursday, January 28, 2010

Right Reasoning, pt. I: Modus Ponens

I’m now taking the time to offer that list of valid forms of arguments promised weeks ago. I’ll offer them one post at a time, due to the space it takes to illustrate and explain them.

As Christians, we are morally obligated to reason correctly. Reliable patterns of reason are reflections of the way God thinks, thus we are to reflect that reality in all our reasoning. The Christian theory of ethics is inextricably tethered to the Christian theory of knowledge (epistemology), which, likewise, is bound-up in the Christian theory of being (metaphysics). If Christ is Lord, he has authority over not only our actions, but our thinking as well, by virtue of Who and What he is. This especially since, our thinking is the loamy soil from which our actions spring, hence revealing what we truly believe.

Valid argument, moreover, is necessary for persuasive, winsome apologetics and evangelism. If a soft-minded unbeliever is persuaded by means of the many invalid arguments Christians often use, while the end may be worth celebration, the means are perfectly unacceptable.

The following will not be an exhaustive list, to be sure; but it is a foundation. Most arguments we (should) use or encounter will roughly follow one form or another.

Not only does knowing and utilizing valid patterns of reasoning help us to frame the message and defense of the gospel in a cogent, truthful way. It also helps us to recognize the fallacious reasoning that inevitably follows in the arguments of the non-Christians working on their own unbelieving presuppositions.

I. Modus Ponens (Latin, lit. “The mode of putting”):

A. Formally stated:

1. If P is the case, then Q is also the case;
2. P is the case;
3. Therefore, Q is also the case.

B. 1 Illustrated from Naturalistic presuppositions:

i. If (P) our brains are a random collection of atoms, responding to various stimuli according to the laws of physics, biology and chemistry, then (Q) true beliefs are illusory, since beliefs are only the consequences of these bits of matter reacting with other bits of matter in ways predetermined by antecedent material causes.

ii. It is, according to Naturalism, the case that (P) our brains are a random collection of atoms, responding to various stimuli according to the laws of physics, biology and chemistry.

iii. Therefore, (Q) true beliefs are illusory, not least a belief in Naturalism.

B. 2. Illustrated from Scripture:

(I.e., Jesus’ response to John the Baptist’s messengers, logically confirming that Jesus was the Coming One, the Messiah. See Matt 11:1—5 // Lk 7:18—22)

i. If I [Jesus] am (P) giving sight to the blind, granting the lame to walk, cleansing lepers, making the deaf to hear, raising the dead, and preaching the good news of the gospel of the Kingdom to the poor, then (Q) I am the One who was to come, the Messiah, since the Old Covenant promised that these works would accompany the Messiah’s ministry.

ii. Tell John what you see and hear, namely that (P) the blind receive their sight, et cetera...

iii. Therefore, John has his assurance; (Q) I am the Messiah, promised in the Old Covenant, whom also his ministry proclaimed.

B. 3 Illustrated from the crux pro-life argument:

i. If (P) the pre-born are innocent human beings, then (Q) non-therapeutic abortion is murder.

ii. (P) The pre-born are innocent human beings (biblically, biologically and embryologically speaking).

iii. Therefore, (Q) non-therapeutic abortion is murder.

C. The fallacy factor:

With respect to modus ponens and modus tollens (see below in next post) there is always the risk of committing a formal fallacy. In the case of modus ponens, we risk the common error of ‘affirming the consequent.’ This needs some explanation.

In logic, the “If...then” construction is known as a conditional statement. Conditionals are then broken into two parts: The antecedent is the “If...” clause, whereas the consequent is the “then...” clause.

In a valid expression of modus ponens, the antecedent is affirmed or asserted in the second premise. However, if the consequent is affirmed, the argument is made invalid and the conclusion doesn’t follow. To use a classic example:

1. If (P) the roads are icy, then (Q) the mail will be late.
2. (Q) The mail is late.
3. Therefore, (P) the roads are icy.

Of course, it is possible that the conclusion is true; the roads may be icy, thus causing the mail to be late. Nevertheless, the conclusion is not the result of a valid, reliable line of reasoning; it’s mere coincidence.

Only months ago, I had a former co-worker argue for the truth of astrology this way.

“Yesterday, my horoscope said (P) that I’d meet an old lover and rekindle the spark. Then, lo and behold, (Q) I ran into ol’ Billy Bob at the bar, and we had a real good time, if you get my drift! How can you doubt the truth of this, then, Kevin? If (P), then (Q); it was the case that (Q), therefore (P) is true!”

I attempted to explain to Debbie that her reasoning didn’t follow; her argument was a non sequitur. She responded. “I don’t know about all your P’s and Q’s, I just know that Billy Bob and I had a real good time!”

D. Valid, yet unsound:

It is quite possible to also use a modus ponens to create a valid argument that is still false. An argument’s validity, as we have labored to show, has to do with following rules and patterns of reliable inference, logical laws. Still, one may produce a false conclusion by means of a valid form of argument. Consider how a nosey neighbor could reason validly, yet end with a false conclusion.

1. If (P) John is late coming home from work, then (Q) John is committing adultery against his wife, Sara.

2. (P) John is late coming home from work!

3. Oh my! (Q) John is having an affair! Quick, call Joan!

The argument follows the valid form of a modus ponens, yet the conclusion is false. The nosey neighbor’s first premise is faulty, the counterfactual being, John had a blow-out on his way home from work. And because a premise on which the conclusion rests is flawed, the conclusion is also flawed; the argument is unsound.

Therefore, we must watch for both a valid form of modus ponens, avoiding the fallacy of affirming the consequent and drawing conclusions from faulty premises, thus avoiding unsoundness. These things we must watch first in our own reasoning and then in the reasoning of others (Matt 7:1—5). For: If we can’t recognize proper patterns of argument in our own reasoning, then neither will we be able to critique that of others...well you should know how the rest goes by now.

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