LOGIC OUTSIDE THE CLASSROOM

Outline

Motivation Mathematics & Fallacies Logic Applied to Faith

Why? How?

Applying Faith to Mathematics

Motivation

Personal background Rejected everything:

Romans 1:21-23: “21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. 22 Although they claimed to be wise, they became fools 23 and exchanged the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles.”

Though that was the wrong approach, accepting everything isn’t the right approach either.

The mathematical approach

In mathematics, we attempt to say only what we mean. If f(x) is differentiable, it is continuous.

If the theorem worked the other way around, we would have said so!

“Usually” is not enough. Sometimes the “full theorem” is not always

known. Though we have suspicions, nothing

more is implied until we write it down and prove it.

Logical Fallacies

Logical fallacies often come because we use our language to disguise the mathematics. Examples:

Ad Hominem Attacking the arguer and not the argument After Sally presents an eloquent and compelling case for a

more equitable taxation system, Sam asks the audience whether we should believe anything from a woman who isn’t married, was once arrested, and smells a bit weird.

Strawman Arguments: Misrepresenting the other side After Will said that we should put more money into health

and education, Warren responded by saying that he was surprised that Will hates our country so much that he wants to leave it defenseless by cutting military spending.

Logical Fallacies

Some come from an outright misunderstanding of mathematics: Gambler’s Fallacy

Forgetting that independent events have separate probabilities

Red had come up six times in a row on the roulette wheel, so Greg knew that it was close to certain that black would be next up. Soon he lost all of his savings.

Slippery Slope Making up false conditional statements to use the

transitive property If we allow pocket knives at public schools, next thing

you know we’ll allow machine guns and everyone will die in a bloodbath.

Applying Logic to our Faith – Why? Wesleyan quadrilateral We are called to do this! 1 Peter 3:15-16: “15 But in your hearts revere

Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect, 16 keeping a clear conscience, so that those who speak maliciously against your good behavior in Christ may be ashamed of their slander.”

Applying Logic to our Faith – Why? 2 Corinthians 10:3-5: “3 For though we live

in the world, we do not wage war as the world does. 4 The weapons we fight with are not the weapons of the world. On the contrary, they have divine power to demolish strongholds. 5 We demolish arguments and every pretension that sets itself up against the knowledge of God, and we take captive every thought to make it obedient to Christ.”

Applying Logic to our Faith – Why? 2 Timothy 4:1-5: “4 In the presence of God and of Christ

Jesus, who will judge the living and the dead, and in view of his appearing and his kingdom, I give you this charge: 2 Preach the word; be prepared in season and out of season; correct, rebuke and encourage—with great patience and careful instruction. 3 For the time will come when people will not put up with sound doctrine. Instead, to suit their own desires, they will gather around them a great number of teachers to say what their itching ears want to hear. 4 They will turn their ears away from the truth and turn aside to myths. 5 But you, keep your head in all situations, endure hardship, do the work of an evangelist, discharge all the duties of your ministry.”

Applying Logic to our Faith – How? Just as in mathematics, we must begin with assumptions. We accept by faith that the Bible is true, so the

statements made in it about God’s character and the nature of our religion are assumed to be true (whether by God or Jesus or David or a prophet or…)

2 Timothy 3:16-17: “16 All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, 17 that the man of God may be complete, equipped for every good work.”

Circular logic – back to the quadrilateral Malachi 3:6 “I the LORD do not change.” Romans 14:23 “… and everything that does not come

from faith is sin.”

Applying Logic to our Faith

Can we assume more statements after the Bible (Tradition)? Do we take the Pope’s word as truth?

…What about C.S. Lewis? …What about modern leaders and pastors?

Kristian Stanfill, “Always” …? Psalms 37:7 “Be still before the LORD and wait patiently for him;

do not fret when people succeed in their ways, when they carry out their wicked schemes.”

Hebrews 6:15 “And so after waiting patiently, Abraham received what was promised.”

2 Peter 3:8-9 “8 But do not forget this one thing, dear friends: With the Lord a day is like a thousand years, and a thousand years are like a day. 9 The Lord is not slow in keeping his promise, as some understand slowness. Instead he is patient with you, not wanting anyone to perish, but everyone to come to repentance.”

Westboro Baptist Church

Testing statements about God

Does it contradict Biblical statements? “God hates homosexuals.”

Romans 5:8 “But God shows his love for us in that while we were still sinners, Christ died for us.”

Can you find a counterexample? “God wants us to be financially successful.”

Mark 12:41-44: 41Jesus sat down opposite the place where the offerings were put and watched the crowd putting their money into the temple treasury. Many rich people threw in large amounts.42 But a poor widow came and put in two very small copper coins, worth only a few cents. 43 Calling his disciples to him, Jesus said, “Truly I tell you, this poor widow has put more into the treasury than all the others. 44 They all gave out of their wealth; but she, out of her poverty, put in everything—all she had to live on.”

Can you extrapolate your own experiences (Experience)? God has made me financially successful, so he wants this for

everybody. (God promised Israelites wealth, Malachi 3) Your personal convictions (drinking, hunting)

Testing statements about God

If you can’t find a counterexample and it seems compatible, does that make it true?

NO! It either follows logically from the

statements we know are true, or we need another reason to believe it (faith, experience, tradition).

Is it worth believing something that might be false? Is it dangerous to believe if it’s false? Do you force the belief upon others?

(Convictions)

Testing statements about God

Is this even okay to do (test statements about God)?

Matthew 4:7: Jesus answered him [Satan], “It is also written: ‘Do not put the Lord your God to the test.’”

But we are not testing God, we are testing the words of people.

Romans 12:2: “Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—his good, pleasing and perfect will.”

Testing statements about God

1 Thessalonians 5:19-22: “19 Do not quench the Spirit. 20 Do not treat prophecies with contempt 21 but test them all; hold on to what is good, 22 reject every kind of evil.”

1 Timothy 3:8-10: “8 In the same way, deacons are to be worthy of respect, sincere, not indulging in much wine, and not pursuing dishonest gain. 9 They must keep hold of the deep truths of the faith with a clear conscience. 10 They must first be tested; and then if there is nothing against them, let them serve as deacons.”

NOTE: The last passage is a “proof by example,” but the other two are not.

Using our assumptions

At the very least, we will assume the statements about God in the Bible are true. How do we use them?

We need to carefully parse the language into statements. (Parables)

We will look at some ways that logic becomes important.

Theorems (God’s promises)

Many “if, then” statements are made in the Bible. We need the entire Bible (at least) as our context.

Remember the truth table for p => q:

Biconditionals

Romans 10:9 “If you declare with your mouth, ‘Jesus is Lord,’ and believe in your heart that God raised him from the dead, you will be saved.” By itself, this statement says that confession that Jesus

is Lord is one way to be saved. It doesn’t say it’s the only way to be saved. Let p: You confess Jesus is Lord and q: You are saved. Then it says p => q.

John 14:6 “Jesus answered, ‘I am the way and the truth and the life. No one comes to the Father except through me.’ ”

This statement says that q => p. Together, the Bible (as a whole) says p <=> q. Without the whole context, we don’t get the complete “theorem.”

Assuming the biconditional

John 14:15 “If you love me, keep my commands.” This is only one direction! Keeping Jesus’

commands alone is not loving him. This is one of the most common

misconceptions of Christianity – that you practice the religion by following a set of rules.

Logical Equivalence

Why all that work? The bible gives many necessary conditions (in mathematical terms) to be loving God:

1 John 4:21: “Anyone who loves God must also love their brother and sister.”

John 14:15 As mentioned, these are not sufficient. Additionally, writing in terms of conditionals

gives us other properties such as the transitive property, and lets us test other conditional statements. If someone says, “If you love God, then you should

hate [some group of people],” they are lying.

Logical Equivalence

Remember that (p => q) is logically equivalent to (~p or q)

“No one can serve two masters. Either you will hate the one and love the other, or you will be devoted to the one and despise the other. You cannot serve both God and money.”

p: You love money. q: You love God. Context is important here! There is an

assumption in the first sentence that you will love one master. Certainly you could hate both. That assumption is not in the second sentence. The argument given can be written as ~(p ^ q) = (~p or ~q) = (p => ~q) = (q => ~p) If you love money, you do not love God. Alternatively: If you love God, you do not love

money.

Does God keep his promises? Titanus 1:1-2: “Paul, a servant of God and an apostle of

Jesus Christ to further the faith of God’s elect and their knowledge of the truth that leads to godliness— 2 in the hope of eternal life, which God, who does not lie, promised before the beginning of time, …”

The word “if” appears 1522 times in the NIV What if you do the “if” of an “if, then” promise of God’s

and God does not keep his end? The only way this makes sense is that you didn’t do it!

1 John 5:14 “This is the confidence we have in approaching God: that if we ask anything according to his will, he hears us.”

Luke 17:6 6 He [Jesus[ replied, “If you have faith as small as a mustard seed, you can say to this mulberry tree, ‘Be uprooted and planted in the sea,’ and it will obey you.

What if the Bible “contradicts” itself?

First and foremost, we accept that the statements in the Bible are true, and we accept that God’s wisdom is far beyond our own: Romans 11:33-36:

Oh, the depth of the riches of the wisdom and knowledge of God!    How unsearchable his judgments,    and his paths beyond tracing out!34 “Who has known the mind of the Lord?    Or who has been his counselor?”35 “Who has ever given to God,    that God should repay them?”36 For from him and through him and for him are all things.    To him be the glory forever! Amen.

Therefore, when we see an apparent contradiction, we know a solution must not exist, even if we can never see it.

What if the Bible “contradicts” itself?

Romans 8:38-39 “38 For I am convinced that neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, 39 neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord.”

Hebrews 6:4-6 “4 It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, 5 who have tasted the goodness of the word of God and the powers of the coming age 6 and who have fallen away, to be brought back to repentance. To their loss they are crucifying the Son of God all over again and subjecting him to public disgrace.”

Possible solutions: Is “love of God” the same thing as “salvation”? (God loves sinners) Who exactly does Hebrews 6:4-6 refer to?

OK to not know the solution? Yes! Good enough for non-believers?

What about when Christians disagree?

Romans 14:1-9: 14 Accept the one whose faith is weak, without quarreling over

disputable matters. 2 One person’s faith allows them to eat anything, but another, whose faith is weak, eats only vegetables. 3 The one who eats everything must not treat with contempt the one who does not, and the one who does not eat everything must not judge the one who does, for God has accepted them. 4 Who are you to judge someone else’s servant? To their own master, servants stand or fall. And they will stand, for the Lord is able to make them stand.5 One person considers one day more sacred than another; another considers every day alike. Each of them should be fully convinced in their own mind. 6 Whoever regards one day as special does so to the Lord. Whoever eats meat does so to the Lord, for they give thanks to God; and whoever abstains does so to the Lord and gives thanks to God. 7 For none of us lives for ourselves alone, and none of us dies for ourselves alone. 8 If we live, we live for the Lord; and if we die, we die for the Lord. So, whether we live or die, we belong to the Lord. 9 For this very reason, Christ died and returned to life so that he might be the Lord of both the dead and the living.

Evangelizing

We need to defend our faith intellectually, through reason as well as experience.

Part of that is an appeal to the experience of the non-believer Romans 1:18-20: 18 The wrath of God is being revealed from

heaven against all the godlessness and wickedness of people, who suppress the truth by their wickedness, 19 since what may be known about God is plain to them, because God has made it plain to them. 20 For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.”

It is imperative that we understand the fundamentals and can defend them – that God loves everyone, that Jesus alone leads to salvation, and so on.

The important things, God has made plain.

Applying Christianity to Mathematics

Unlike science, our profession gives evidence to the existence of God.

Was the Pythagorean Theorem true before it was written down?

Every mathematical theorem is one of God’s promises, too.

Studying them is an act of worship. God chooses what mysteries to reveal to us.

(verse?) Approach your study prayerfully.

Conclusion

Logic is important for everyday decisions, as well as for our faith.

Approach your study of mathematics worshipfully!