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Grace Bible Church

4000 E. Collins Rd.   P.O. Box #3762   Gillette, WY  82717   (307) 686-1516

 

- Preaching the Living WORD through the Written WORD - 2 Tim 4;:2 -

 

 

 

 

INTRO TO LOGIC AND THE BIBLE

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     INTRODUCTION TO LOGIC

 

A.    Logic is the instrument (Aristotle’s collection, Organon; organon - “instrument”) by which we reason and by which all sciences operate. Aristotle is credited with defining “logic,” not inventing it. God is the source of logic, making it self-evident from His nature (See Diagram).

 

 

B.    God communicates with man through reason in Scripture. Therefore, logic is essential in understanding and interpreting the Scriptures. Note the various quotes:

1.     The whole counsel of God, concerning all things necessary for his own glory, man’s salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture:  unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men. (Westminster Confessions of Faith 1:6)

2.     Reason is the instrument of discovery of all doctrines and duties, whether ‘expressly set down in Scripture’ or ‘by good and necessary consequence deduced from Scripture’:  but their authority, when once discovered, is derived from God, who reveals them and prescribes them in Scripture, either by literal assertion or by necessary implication. (B. B. Warfield on the Confession)

3.     When we accept the laws of logic, we are not accepting laws external to God to which he must be subject, but we are accepting laws of truth which are derived from God’s holy character. (James O. Buswell)

4.     The science of reasoning is of very great service in searching into and unraveling all sorts of questions that come up in Scripture….The validity of logical sequences is not a thing devised by men, but it is observed and noted by them that they may be able to learn and teach it; for it exists eternally in the reason of things, and has its origin with God. (Augustine)

5.     Logic is fixed, universal, necessary, and irreplaceable…[because] God is a rational being, the architecture of whose mind is logic. (Gordon Clark)

 

II.    DEFINITIONS OF LOGIC

 

A.    Logic is the science of reasoning.

B.    Logic is the science of necessary inference.

C.    Logic is thinking clearly without contradictions or fallacies.

D.    Logic is the rules governing right reasoning; the study of the methods and principles to distinguish good (valid) reasoning from false (invalid).

E.    Logic is the branch of philosophy that deals with the forms of thinking in general, and more especially of inference, of scientific method, and the art of reasoning and that system of rules for convincing or confounding an opponent by argument.

 

III.  DISTINCTIONS IN LOGIC

 

A.    The concept of logic is basic to all thinking, reasoning, and sciences. However, there are several distinctions in logic within different sciences (Mathematics, Scientific, and Dialectical (Speech) etc.). The particular focus of logic in this class will be Dialectical Logic. It is sometimes called Propositional Logic or Sentential Logic.

B.    Dialectical Logic is the study of rules for arguments in propositions or statements. In a sense, Dialectical Logic is the basis for all other sciences because most ideas are communicated through words.

C.    There are two basic types of logic in Dialectical Logic; they are “Formal Logic” and “Informal Logic.”

1.     Formal Logic involves the validity and certainty of an argument based on the structure of statements (premises and conclusions).

2.     Informal Logic involves the strength and probability of an argument based on the support of statements (premises and conclusions).

 

IV.  INFORMAL FALLACIES

 

Intro to Informal Fallacies:

1.     Definitions of an Argument

a)    An argument is offering a set of reasons or evidence in support of a conclusion (Informal Logic).

b)    An argument is a connected series of statements intended to establish a definite proposition. (Formal Logic) (Monty Python, Argument Clinic)

2.     Definition of a Fallacy

a)    A fallacy is a type of incorrect argument. They are not formal or technical in nature.

b)    Informal fallacies in logic can be caused by inattentiveness, carelessness, fatigue, prejudice, bias, ignorance, and the sin nature.

c)     A typical fallacy arrives at irrelevant conclusions. In other words, it is an argument that does not establish what it intends to establish.

A.    Appeal To Force

1.     It is argument by intimidation, scare tactics, or force. It is also called “Argumentum Ad Baculum” (“argument to the stick”).

2.     This line of "reasoning" is fallacious because coercing people through intimidation does not constitute evidence for a claim.

3.     Ex. “You had better agree that the new company policy is the best if you expect to keep your job.”

4.     Ex. “The defendant ought to be found innocent because if he isn't, there will be a riot and many innocent citizens will be hurt or killed.”

5.     It is seen of wicked rulers in the Bible (Pr 28:15).

6.     It is used by Satan to cause believers to fear and falter (1Pe 5:8-9).

7.     It could be used by wealthy individuals in the church who withhold funds if their view is not accepted.

8.     It could be used by pastors to intimidate and ridicule those who do not agree with his views.

B.    Personal Attack

1.     It is argument by attacking the man (Ad Hominem Abusive - ad hominem - “to the man”).

2.     The reason why an Ad Hominem Abusive is a fallacy is that the character, circumstances, or actions of a person do not have a bearing on the truth or falsity of the claim being made.

3.     Ex. “Candidate Jane Jones' proposal X is ridiculous. She was caught cheating on her taxes in 2003.”

4.     Ex. “We should disregard Fred's argument because he is just angry about the fact that the defendant once cheated him out of $100.”

5.     It was used against Jesus to disregard his teaching (Mat 12:24f).

6.     It is often associated with “name calling.”

7.     It could be used in debates regarding religion by both sides.

8.     An ad hominem attack often resorts to “name calling” because they cannot defeat the argument any other way.

C.    Appeal To Emotions

1.     It is an argument that appeals to emotion rather than reason.

2.     This fallacy is committed when someone manipulates peoples' emotions in order to get them to accept a claim as being true.

3.     This fallacy is actually an extremely effective persuasive device. As many people have argued, peoples' emotions often carry much more force than their reason. Logical argumentation is often difficult and time consuming and it rarely has the power to spurn people to action. An appeal to emotions is very powerful which explains why it is popular and used widely.

4.     Ex. “Bill goes to hear a Democrat speak. The Democrat tells the crowd about the evils of the Republicans, such as taking away Social Security, not caring about teachers and education, not doing anything about Global warming. After hearing the speech, Bill is incensed with the Republican Party. He feels good about joining the Democratic Party and accepts it is as the right thing to do.”

5.     Ex. "It was so great to worship with you last Sunday night. The songs were great, and the band helped me to worship God. I appreciate the way you recognize people's emotions and include an appeal to emotions."

6.     Appeal to emotion was used by Jewish religious leaders to incite retaliation (Mt 5:38, 43).

7.     While it is not wrong for preachers to stir the listeners to action, they must do so by appealing  to reason through the Scriptures (Is 1:18; Ac 17:2, 17; 18:4, 19; 19:9). Emotions do not necessarily generate correct beliefs or correct responses.

D.    Appeal To Popularity

1.     It is an argument that appeals to popular demand rather than facts and evidence.

2.     The basic idea is that a claim is accepted as being true simply because most people are favorably inclined towards the claim.

3.     At one time people approved of claims such as "the world is flat", "humans cannot survive at speeds greater than 25 miles per hour", "the sun revolves around the earth" but all these claims turned out to be false.

4.     This sort of "reasoning" is quite common and can be quite an effective persuasive device. Since most humans tend to conform with the views of the majority, convincing a person that the majority approves of a claim is often an effective way to get him to accept it. Advertisers often use this tactic when they attempt to sell products by claiming that everyone uses and loves their products.

5.     Ex. “I read the other day that most people would really like to see gun owners disarmed. I have always liked guns, but if most people don’t like them they must be right.”

6.     Sometimes Christians adopt the popular views of the world (1Co 15:33; 1Jo 2:16) or adopt certain Bible interpretations simply because most Christians hold to them.

E.    Appeal To Tradition

1.     It is an argument that appeals to the old way of doing things not necessarily because it is right.

2.     This sort of "reasoning" is fallacious because the age of something does not automatically make it correct or better than something newer. On the other hand, new (Appeal To Novelty) is not always better either.

3.     However, if someone successfully argues why something has stood the test of time, it would be backed by evidence and not be a fallacy.

4.     Ex. Reporter: "Mr. Hatfield, why have you been fighting with the McCoys all these years? Hatfield: "I don't rightly know. I'm sure it was the McCoys who started it all, though." Reporter: "If you don't know why you're fighting, why don't you just stop?" Hatfield: "Stop? What are you crazy? This feud has been going on for generations so I'm sure there is a good reason why it started. So I aim to keep it going.”

5.     The Pharisees neglected the correct biblical course because they held to the traditions of men (Mk 7:8 cp. Col 2:8).

6.     While believers must not hold to the traditions of men, there are some valid biblical traditions (1Co 11:2; 2Th 2:15).

F.     Appeal To Authority

1.     It is an argument that bases its appeal on a person who is not an authority in that field.

2.     This fallacy is committed when the person in question is not a legitimate authority on the subject.

3.     When a person falls prey to this fallacy, they are accepting a claim as true without there being adequate evidence to do so. More specifically, the person is accepting the claim because they erroneously believe that the person making the claim is a legitimate expert and hence that the claim is reasonable to accept.

4.     Since people have a tendency to believe authorities (and there are, in fact, good reasons to accept some claims made by authorities) this fallacy is a fairly common one.

5.     Ex. “I'm not a doctor, but I play one on TV. When you get a bad cough, you need Vicks Adult Formula 44. You can’t buy anything more effective.”

6.     Commercials use this all the time when athletes support their product.

7.     Some individuals in authority believe they are an authority in every field.

G.    Appeal To Ignorance (Burden of Proof)

1.     It is an argument that is based on a lack of evidence.

2.     It is also known as the burden of proof. It becomes a fallacy when the burden of proof is placed on the wrong side.

3.     For example, in the United States an individual is innocent until proven guilty. Therefore the burden of proof is on the prosecution, not the defense.

4.     Ex. Bill: "I think that some people have psychic powers." Jill: "What is your proof?" Bill: "No one has been able to prove that people do not have psychic powers."

5.     It is an erroneous argument for Christians to say, I believe there is a God because no one has ever proved that God does not exist.

6.     There are biblical, scientific, and philosophical reasons why God exists and Christians should know how to use them.

7.     Atheists often claim that they have no burden of proof to prove that God does not exist. In one sense, that is true. However, when they make the claim that God does not exist, which they often do, then a burden of proof rests upon them to substantiate their claim.

H.    Poisoning the Well

1.     It is an argument that includes unfavorable information (true or false) about the opponent not related to the issue.

2.     The person making such an attack is hoping that the unfavorable information will bias listeners against the person in question and hence that they will reject any claims he might make.

3.     However, merely presenting unfavorable information about a person (even if it is true) hardly counts as evidence against the claims he/she might make.

4.     This was the Pharisees fallacious attempt to thwart Jesus’ teaching (Luk 15:2). But wisdom and truth is based on facts and evidence (Mat 11:19).

5.     This is akin to the church member that attempts to taint someone’s reputation in order to get others to reject his ideas.

I.     Straw Man

1.     It is an argument that ignores a person's actual position and substitutes a distorted, exaggerated or misrepresented version of that position.

2.     It could also be defined as skewing an opponent’s argument so that it can be easily defeated.

3.     This sort of "reasoning" is fallacious because attacking a distorted version of a position simply does not constitute an attack on the position itself.

4.     Ex. "Senator Jones says that we should not fund the attack submarine program. I disagree entirely. I can't understand why he wants to leave us defenseless like that."

5.     A straw man argument was used by those who slanderously falsified Paul’s beliefs (Rom 3:8). Also cp. Act 6:13-14.

J.     Red Herring

1.     It is an argument in which an irrelevant topic is presented in order to divert attention from the original issue.

2.     It is also called a “smoke screen” or “wild goose chase.” Instead of concentrating on all the white herring, one is distracted by one red herring.

3.     The basic idea is to "win" an argument by leading attention away from the original issue to another issue.

4.     Ex. “We admit that this policy is popular. But we also urge you to note that there are so many policies on this ballot that the whole thing is getting ridiculous.”

5.     This sort of "reasoning" is fallacious because merely changing the topic of discussion hardly counts as an argument against a claim.

K.    Special Pleading

1.     It is an argument which gives one-sided evidence while omitting other relevant facts that may lead to another conclusion.

2.     This is similar to the fallacy of “double standard” where a person applies a standard to an opponent’s argument but has a special case for not applying it to his own.

3.     Ex. I know that nine out of ten studies show a different conclusion, but this one study argues my case.”

4.     Ex. "In the Thomistic cosmological argument for the existence of God, everything requires a cause. However, proponents of the argument then create a special case where God doesn't need a cause, but they can't say why in any particularly rigorous fashion." (Thomas Aquinas did not say everything has a cause. Rather, he said every effect ("efficient cause") has a cause. It is not possible to regress to infinity in efficient causes. Therefore, an uncaused First Cause exists and this is God).

5.     Ex. “The Bible is like any other mythological literature portraying fictitious gods.” (Actually the Bible is one of the most credible historical documents ever written. Its characters verifiably existed and its events are historically recorded by outside sources.)

6.     The Jews used special pleading to suggest Paul was persuading “men to worship God contrary to the law” (Ac 18:13-16).

L.    Slippery Slope

1.     It is an argument that asserts that an action will initiate a chain of events culminating in an undesirable event later.

2.     In some cases, the assumption is made that one event immediately leads to an exaggerated or catastrophic event.

3.     Ex. “Give them an inch and they’ll take a foot!”

4.     Ex. “We have to stop the tuition increase! The next thing you know, they'll be charging $40,000 a semester!”

5.     The Pharisees used a slippery slope fallacy when stating that if they did not kill Jesus, the Romans would take away their nation (Joh 11:48).

M.   Relativistic Fallacy

1.     The relativist fallacy, also known as the subjectivist fallacy, is a fallacy committed when one person claims that something may be true for one person but not true for someone else.

2.     It is an argument that rejects a claim by asserting that the claim might be true for others but is not for him/her.

3.     Regarding fallacies, relativism is the view that truth is relative to a person, time, culture, place, etc.).

4.     It is not a fallacy when dealing with preferences, personal tastes, or with subjective experiences, but only with objective truth.

5.     This is the idea of the biblical quotation, “everyone did right in his own eyes” (Jdg 17:6; 21:25; Pr 12:15; Pr 21:2)

N.    False Dilemma

1.     It is an argument that assumes there are only two alternatives when in fact there are more than two.

2.     Sometimes there are only two alternatives, but always assuming that there are only two is fallacious.

3.     Some people insist that if you disagree with them on one issue, then you must be against everything they stand for.

4.     Ex. “Either you give to this needy person or you are a greedy capitalist.”

5.     A False Dilemma fallacy was used against Jesus in regard to giving to Caesar (Mt 22:16-22) and the resurrection (Mt 22:23-33).

O.    Begging the Question (Circular Argument)

1.     It is an argument that includes the conclusion in one of the premises.

2.     It is also called Circular Reasoning, Reasoning in a Circle, Petitio Principii.

3.     This sort of "reasoning" is fallacious because it continuously asserts a claim but never proves or brings it to a satisfactory conclusion.

4.     Some cases of question begging are fairly blatant, while others can be extremely subtle.

5.     The Christian cannot correctly argue, “The Bible is inspired because the Bible says that it is inspired.” The common response is, “So does the Koran.”

6.     You would expect inspired writings to declare their own inspiration. But self-authentication does not give proof of inspiration.

7.     We could argue miracles confirmed God’s spokesmen. God’s spokesmen speak the words of God infallibly. God’s spokesmen infallibly declare the Bible is inspired.

P.     You Too Fallacy

1.     It is an argument that asserts that a certain position is wrong because its proponent fails to consistently act in accordance with that position.

2.     It is an argument that rejects a position because the opponent is guilty of the same wrongdoing (“you too” - “tu quoque”).

3.     Also, the fact that a person's claims are not consistent with his own actions might indicate that the person is a hypocrite but this does not prove his claims are false.

4.     Another version of the “you too” fallacy is when Party A is asked to defend the actions of Politician A. Their response to Party B is that Politician B was also guilty of the same actions. True or not, this response never sufficiently defended Politician A’s actions. Besides, if Politician B’s actions were also wrong, two wrongs do not make a right (arguing against the fallacy of “Two Wrongs Make a Right”).

Q.    Bandwagon

1.     It is an argument in which a threat of rejection by one's peers is substituted for evidence in an "argument."

2.     It is also known as, “peer pressure.”

3.     The strength of this fallacy rests on the fact of that everyone has the need to belong. This sometimes becomes a strong emotional appeal to conform to the views and positions of those groups even if wrong.

4.     Keep in mind that there is a difference between compromising truth and compromising preferences for the sake of peace.

5.     Lk 6:26 - Woe to you when all men speak well of you, for their fathers used to treat the false prophets in the same way.

R.    Post Hoc

1.     The full name is "Post hoc, ergo propter hoc," which means, "After this, therefore because of this." This is a sequential fallacy.

2.     It is an argument that asserts that one event is caused by another event, simply because it preceded it. A preceded B, therefore, A caused B.

3.     Ex. “Joan is scratched by a cat while visiting her friend. Two days later she comes down with a fever. Joan concludes that the cat's scratch must be the cause of her illness.”

4.     Ex. “Party A passes a new tax reform law that benefits upper class Americans. Shortly thereafter the economy takes a nose dive. Party B claims that the tax reform caused the economic woes and they push to get rid of it.”

5.     Ex. “Acts 2:4 teaches that the apostles received the Holy Spirit and began to speak in tongues. Therefore, the Bible teaches that everyone who receives the Holy Spirit will speak in tongues.” (There are passages that teach that not every believer will speak in tongues (1Co 12:29-30)

6.     Two similar fallacies are “Confusing a Common Cause,” and “Ignoring a Common Cause.”

S.     Equivocation (Ambiguity)

1.     It is an argument that occurs when a word or phrase is used with two or more meanings. In fact, ambiguity is one of the seven deadly sins of correct thinking.

2.     Ex. “If all men are created equal, then why are pro basketball players so tall?”

3.     Ex. “Your argument is sound; nothing but sound.”

4.     Amphibole (or Relationship) is one where the words are clear but the grammatical construction is not.

5.     Ex. “Save soap and waste paper.” or “I live by the river; drop in some time.”

6.     Accent (or Emphasis) occurs when the accent, emphasis, or tone of voice changes the meaning.

7.     Ex. “You have heard that it was said, ‘You shall love your neighbor, and hate your enemy’” (Mt 5:43). or “I love you.” “I love you.” “I love you.” “I love you.”

8.     Significance (or Circumstance) is committed when conditions or circumstances change the meaning of the words.

9.     Ex. “What is truth?” (by a philosophy student) or “What is truth?” (Pontius Pilate)

10.  Ex. “Son of God” (God incarnate) or “Son of God” (highest created being - JW’s)

T.    Non Sequitur - drawing a conclusion that does not follow (unwittingly or on purpose).

 

V.    THREE BASIC LAWS OF LOGIC

 

A.    Three Basic Laws

 

1.     These fundamental laws are true principles governing reality and thought and are assumed by Scripture. Some claim they are arbitrary Western constructions, but this is false. The basic laws of logic govern all reality and thought and are known to be true for at least two reasons: (1) They are intuitively obvious and self-evident. Once one understands a basic law of logic (see below), one can see that it is true. (2) Those who deny them use these principles in their denial, demonstrating that those laws are unavoidable and that it is self-refuting to deny them. (J.P. Moreland, Three Laws of Logic)

2.     The basic laws of logic are neither arbitrary inventions of God nor principles that exist completely outside God’s being. Obviously, the laws of logic are not like the laws of nature. God may violate the latter (say, suspend gravity), but He cannot violate the former. Those laws are rooted in God’s own nature. Indeed, some scholars think the passage “In the beginning was the Word [logos]” (Jn 1:1) is accurately translated, “In the beginning was Logic (a divine, rational mind).” For example, even God cannot exist and not exist at the same time, and even God cannot validly believe that red is a color and red is not a color. Often God does not act in ways that people understand or judge to be what they would do in the circumstances. But God never behaves illogically in the proper sense. He does not violate in His being or thought the fundamental laws of logic. (ibid.)

 

B.    Law of Identity - “A is A” (A = A)

 

1.     In other words, A is A, and cannot be anything but A.

2.     “...a thing is itself… the fact or the existence of the thing must already be evident… each thing is inseparable from itself” (Aristotle, Metaphysics Book VII, Part 17)

3.     The law of identity says that if a statement such as “It is raining” is true, then the statement is true. More generally, it says that the statement P is the same thing as itself and is different from everything else. Applied to all reality, the law of identity says that everything is itself and not something else. (J.P. Moreland, Three Laws of Logic)

4.     This emphasizes the importance of understanding and defining our terms. Without such identification, all communication would be impossible and nonsensical (1Co 14:8-11).

5.     This law is not above God, but comes from the essence of God’s nature, including all His attributes. God revealed Himself to Moses as “I AM WHO I AM” (Ex 3:14). God is Who He is, from His nature He acts as He acts. Therefore, truth and reality are what they are because God is the eternal, self-existent, divine creator.

6.     See also Jn 6:48; 8:12; 10:11; 11:25; 14:6; 15:1; Re 22:13.

 

C.    Law of Non-Contradiction - “A cannot be both A and not A”  ~(A & ~A)

 

1.     It is impossible for the same thing at the same time to belong and not belong to the same thing at the same time and in the same respect. (Aristotle, Metaphysics 1005b12-20). Or simplified, A cannot be A and non-A at the same time and same respect.

2.     The law of noncontradiction says that a statement such as “It is raining” cannot be both true and false in the same sense. Of course it could be raining in Missouri and not raining in Arizona, but the principle says that it cannot be raining and not raining at the same time in the same place. (J.P. Moreland, Three Laws of Logic)

3.     A contradiction is two opposing statements. A paradox (classical definition) is something which appears to be a contradiction but is not.

4.     Because God is Who He is and is a God of truth, it is impossible for God to lie, say something false, or contradict Himself (He 6:18; Tit 1:2; Nu 23:19). Therefore, there can be no lie or contradiction in the truth (1Jn 2:21). If God contradicted Himself, communication from God would be impossible and nonsensical. When He gave the command to Adam and Eve not to eat from the tree of knowledge of good and evil, it did not mean that they could also eat from the tree of knowledge of good and evil (Ge 2:17).

5.     The orthodox Christian view of the Trinity is not a contradiction. It is not claimed that God is one God and also three Gods at the same time in the same respect. Rather, the Trinity is explained in that God is one in essence but subsists in three persons.

6.     Until a little more than a hundred years ago, the law of contradiction was almost universally accepted by philosophers as a self-evident truth. Francis Schaeffer attributed the decline of 20th-century society to the demise of the law of contradiction. He suggested that when philosophy abandons this principle it sinks beneath "the line of despair" and ultimately makes suicide the only viable course of action. (Phil Johnson, The Law of Contradiction)

7.     On a positive note, when we are engaged in defending the faith, and someone denies this law, the debate is over. Why do I call this a “positive note”? Because if a person claims their disbelief in rationality or logic as a reason for not believing in Christianity, then they have made the case for Christianity. As we defend Christianity we are trying to demonstrate that every alternative to apostolic doctrine is an exercise in irrationality. If the only way one can escape from belief in God is by denying logic, then so be it. (Sproul, R.C., Defending Your Faith)

 

D.    Law of Excluded Middle - “A must be either A or not A” (A v ~A)

 

1.     In other words, A must be either A or not A. Any middle alternative is excluded.

2.     The law of the excluded middle says that a statement such as “It is raining” is either true or false. There is no other alternative. (J.P. Moreland, Three Laws of Logic)

3.     The law of excluded middle says that a statement is true or false. Or it can be said that of two contradictory statements one is true while the other is false.

4.     This is observed in the essence of God, “with whom there is no variation or shifting shadow” (Jm 1:17). God is either good or He is evil. There is no middle alternative that God is both good and evil. Therefore, since God is good, He cannot be evil (Jm 1:13).

5.     Let what you say be simply 'Yes' or 'No'; anything more than this comes from evil (Mt 5:37 ESV).

6.     It is either right to obey God rather than man or it is not right. You be the judge (Ac 4:19).

7.     Either Jacob was Isaac’s son Esau or he was not Isaac’s son Esau (Ge 27:21).

8.     Israel either kept God’s commands or they did not keep God’s commands (Dt 8:2; Jdg 2:22).

9.     John exhorted believers to test the spirits. Either they were from God or they were not from God (1Jn 4:1).

10.  This is not to be confused with the fallacy of “False Dilemma” (also known as fallacy of “Excluded Middle”).

 

VI.  FORMAL LOGIC

 

A.    Informal Logic pertains to the strength of an argument while Formal Logic involves the validity and certainty of an argument based on the structure of statements (premises and conclusions). In other words, Formal Logic specifically concentrates on the forms of an argument.

B.    The basic and standard forms are called “categorical statements.”

C.    A categorical statement is a statement that relates two classes (set of things) or categories.

D.    Categorical statements are used to determine identity, contradiction, excluded middle. They are also used to determine premises and conclusions in categorical syllogisms, rules of inference, and informal arguments.

E.    There are four different standard forms of categorical statements represented by the following symbols: A, E, I, O.

F.     These labels come from the medieval period when logic was studied in Latin. The letters are vowels from the Latin words A F F I R M O and N E G O, meaning (respectively) “I affirm” and “I deny.”

 

1.     A - “all,” 

2.     E - “no,”  

3.     I - “some,” 

4.     O - “some (are) not”

 

G.    To be in standard form, the elements of a categorical statement must appear in the following order:

 

1.     Quantifier (i.e., the word “all “no,”  “some,” or “some (are) not”)

2.     Subject term (i.e., a word or phrase that names a class or category)

3.     Copula (“to be” verb - “is” and “are” or “is not” and “are not”)

4.     Predicate term (i.e., a word or phrase that names a class or category)

 

            Ex. “All S are P,” = All (quantifier) S (subject) are (copula) P (predicate).

            Ex. “All men are mortal,” = All (quantifier) men (subject) are (copula) mortal (predicate).

 

H.    The four standard forms are as follows:

 

1.     (A)  - “All S are P”  (universal affirmative)

a)    All men (S) are mortal (P).

b)    All beagles (S) are dogs (P).

c)     All Scripture is inspired (God-breathed) (2Ti 3:16).

d)    All men (S) are sinners (P) (Rom 3:23).

e)     Everyone who calls on Christ is a person who is saved (Rom 10:13).

f)     Any who believe in Christ are those who have eternal life (Joh 3:16).

g)     Only those in Christ are those who possess all spiritual blessings (Eph 1:3).

 

2.     (E)  - “No S are P”  (universal negative)

a)    No men (S) are immortal (P).

b)    No beagles (S) are cats (P).

c)     No men (S) are righteous (P) (Ro 3:10).

d)    No unsaved men are those who understand spiritual things (Ro 3:11a)

e)     No unsaved men are those who seek God (Ro 3:11b).

f)     Nothing unclean is that which enters heaven (Re 21:27).

 

3.     (I)   - “Some S are P” (particular affirmative)

                                                                  

a)    Some men (S) are Professors (P)

b)    Some trees (S) are oaks (P)

c)     Some believers are evangelists (Ep 4:11).

d)    Some believers are teachers (Ep 4:11).

e)     Some who have died are those who have seen Christ (1Co 15:6).

 

4.     (O) - “Some S are not P” (particular negative)

                         

a)    Some graduates (S) are not Doctors (P)

b)    Some trees (S) are not oaks (P)

c)     Some who descended from Israel are not believers (Ro 9:6).

d)    Some who say Lord, Lord are those who will not enter heaven (Mt 7:21).

 

I.     Translating normal sentences into categorical statements

 

1.     To translate a sentence into a categorical statement do the following:

1)    Determine the quantifier and subject category.

2)    Insert the copula (is/are).

3)    Add the predicate category.

4)    Note: Commands and questions are not propositions and cannot be translated into categorical statements

2.     Examples of translating categorical statements

a)    Everybody can throw a ball.

(1)   All people are ball-throwers. (A)

b)    Some college students will not become Professors.

(1)   Some college students are persons who will not become Professors. (O).

c)     “Some, to be sure, are preaching Christ even from envy” (Php 1:15).

(1)   Some persons are persons who are preaching Christ from envy. (I)

d)    “nor any other created thing, will be able to separate us from the love of God” (Ro 8:39).

(1)   No created things are things that can separate us from the love of God. (E)

e)     “But a man named Ananias, sold a piece of property” (Ac 5:1)

(1)   All persons identical to Ananias are persons who sold their property. (A)

f)     “Why has Satan filled your heart to lie to the Holy Spirit?” (Ac 5:3).

(1)   Not a statement but a question

g)     “Therefore repent and return” (Ac 3:19).

(1)   Not a statement but a command.

h)    *Socrates is a man.

(1)   All persons identical to Socrates are persons who are men. (A)

i)      *Everything that begins to exist has a cause.

(1)   All things that begin to exist are things that have a cause. (A)

 

                                                  *(simplified form that is an acceptable standard form)

 

3.     Stylistic variants of categorical statements

a)    A - Universal Affirmative (All S are P)

(1)   Every S is a P.

(2)   Each S is a P.

(3)   Any S is a P.

(4)   If anything is an S, then it is a P.

(5)   Things are S only if they are P.

(6)   Only P are S.

b)    E - Universal Negative (No S are P)

(1)   Nothing that is an S is a P.

(2)   A thing is an S only if it is not a P.

(3)   If anything is an S, then it is not a P.

(4)   Nothing is an S unless it is not a P.

c)     I - Particular Affirmative (Some S are P)

(1)   There are S that are P.

(2)   At least one S is a P.

(3)   There exists an S that is a P.

(4)   Something is both an S and a P.

d)    O - Particular Negative (Some S are not P)

(1)   At least one S is not a P.

(2)   Not all S are P.

(3)   Not every S is a P.

(4)   Something is an S but not a P.

(5)   There is an S that is not a P.

4.     Examples of translating categorical statements

a)    “Not everyone who says to Me, 'Lord, Lord,' will enter the kingdom of heaven” (Mt 7:21)

(1)   Some persons who say “Lord, Lord” are persons who will not enter heaven (O).

b)    “everyone who does evil hates the Light” (Jn 3:20)

(1)   All those who do evil are those who hate the Light (A)

c)     “but not all things are profitable” (1Co 10:23)

(1)   Some things are things that are not profitable (O)

d)    If anyone wishes to come after Me, he must deny himself” (Lk 9:23)

(1)   All persons who wish to come after Me are persons who must deny themselves” (A).

e)     “only there are some who are disturbing you” (Ga 1:7)

(1)   Some persons are persons who are disturbing you (I).

f)     “No one has seen God at any time” (Jn 1:18)

(1)   No persons are persons who have seen God” (E).

g)     “But there are some of you who do not believe” (Jn 6:64)

(1)   Some persons are persons who do not believe (O).

h)    “There is now no condemnation for those who are in Christ Jesus” (Ro 8:1).

(1)   All persons who are in Christ are persons who will not receive condemnation. (not in standard form)

(2)   No persons who are in Christ are persons who will receive condemnation. (standard form E)

 

VII. THE SQUARE OF OPPOSITION

 

A.    Inference - An inference is the process of drawing (inferring) a conclusion from a statement or premise.

B.    Immediate Inference - an immediate inference is when a conclusion is drawn from only one premise.

C.    The Square of Opposition - is a way of diagramming logical relations and immediate inferences between categorical statements (A, E, I, O).

 

 

D.    Explanation of Square of Opposition

1.     Contradictories (A ←→ O and  E ←→ I) are statements that cannot both be true (or false). For example, “All dogs are collies” contradicts “Some dogs are not collies” and vice versa. Also, “No dogs are collies” contradicts “Some dogs are collies” and vice versa.

2.     Contraries (A ←→ E) are statements that cannot both be true but they can both be false. For example, “All dogs are collies” and “No dogs are collies” are contraries and cannot both be true. If one of these statements is true, the other must be false. But if in fact only “Some dogs are collies,” they are both false.

3.     Subcontraries (I ←→ O) are statements that cannot both be false but they can both be true. For example, “Some dogs are collies” and “Some dogs are not collies” can both be true (“some are” and “some are not”). But if in fact “All dogs are collies,” then only “Some dogs are collies” is true.

4.     Implications are made from statements such as, A → I (“All ants are insects” implies “Some ants are insects.”), and E → O (“No ants are antelope” implies “Some ants are not antelope.”). We can only consider that I → A (Some ants are insects” implies “All ants are insects”) might be true, if we do not know that “All ants are insects.” But if in fact only “Some ants insects” then “All ants are insects” would be false.

E.    Exercise to determine the immediate inference (First statement is assumed true)

1.     All successful executives are intelligent men.

a)    No successful executives are intelligent men.

b)    Some successful executives are intelligent men.

c)     Some successful executives are not intelligent men.

2.     No animals with horns are carnivorous.

a)    Some animals with horns are carnivorous.

b)    Some animals with horns are not carnivorous.

c)     All animals with horns are not carnivorous.

F.     Exercise to determine validity of immediate inferences. (First statement is assumed true)

1.     All cougars are carnivores. So, it is false that some cougars are not carnivores.

2.     All legal treaties are promises. Hence, it is not the case that no legal treaties are promises.

3.     Some mosquitoes are evil beings. Therefore, it is not true that no mosquitoes are evil beings.

4.     All self-absorbed people are boring people. It follows that some self-absorbed people are boring people.

5.     Some lawyers are shysters. So, all lawyers are shysters.

6.     No five-star generals are humble people. Consequently, it is false that some five-star generals are humble people

 

VIII.       CATEGORICAL SYLLOGISMS

 

A.    Syllogisms

1.     A syllogism, in logic, is a mode of deductive reasoning that consists of a sequence of three propositions; two premises and one conclusion.

2.     Aristotle’s formulations of syllogistic logic held sway in the Western world for over 2,000 years. Since the 19th Cent., Aristotelian logic has been supplanted by symbolic logic, which replaces ordinary language with mathematical symbols. However, linguistic syllogisms (categorical) remain a verifiable means of valid inference.

3.     The classic example of a syllogism is:

1. All men are mortal (Premise #1).

2. Socrates is a man (Premise #2).

3. Therefore, Socrates is mortal (Conclusion).

4.     A syllogism can be visualized by the Euler Circle:

5.     The previous syllogism is a “valid” syllogism (correct form). A valid syllogism is a syllogism that is in standard form (correct) in which case the conclusion necessarily (certain or guaranteed) follows. For a syllogism to be “sound,” the form must be valid (correct) and the premises must be true (discussed later).

6.     Therefore, if Premise #1 and #2 are in the correct form, then it is logically “necessary” (certain or guaranteed) that the conclusion must follow.

7.     So, if “All men are mortal” and “Socrates is a man” are in the correct form, then it is logically “necessary” (certain or guaranteed) that “Socrates is mortal.

8.     Not all syllogisms are “valid.” Invalid syllogisms are not in correct form and therefore do not guarantee that the conclusion necessarily follows. Note the following syllogism:

1. All dogs are mammals (Premise #1).

2. All cats are mammals (Premise #2).

3. Therefore, all cats are dogs (Conclusion).

        

9.     Even though Premise #1 and #2 may be true, the syllogism is not in correct form. Therefore, the conclusion does not necessarily follow and is invalid. Furthermore, the syllogism is not sound.

B.    Standard Forms of Moods

1.     To determine the form of a syllogism, we must understand the moods, terms, and figures.

2.     Our example syllogism is in the mood of “AAA,” which is the most utilized and the most simplified. Statements 1, 2, and 3 are all “A” propositions (All S are P).

1. All men are mortal. (A)

2. Socrates is a man.    (A)

3. Socrates is mortal.   (A)

3.     The following is an EIO form.

1. No heroes are cowards.

2. Some soldiers are cowards.

3. Some soldiers are not heroes.

4.     The following is an AEE form.

1. All kings are princes.

2. No princes are princesses.

3. No princesses are kings.

5.     The following is an IAI form.

1. Some students are Freshmen.

2. All students are enrolled.

3. Some enrolled are Freshmen.

C.    Standard Forms of Terms

1.     To determine the form of a syllogism we must know the “major term,” “minor term,” and “middle term.” The major term becomes the predicate (P) and the minor term becomes the subject (S).

1. All men (mid) are mortal (maj).  -        men        mortal      -     M     P

2. Socrates (min) is a man (mid).    -     Socrates     men        -    S    M

3. Socrates (min) is mortal (maj).   -     Socrates    mortal      -    S     P

2.     The standard form of major, minor, and middle terms are as follows:

a)    The major term (P) should be in line 1.

b)    The minor term (S) should be in line 2.

c)     The middle term (M) should be in both line 1and 2.

d)    The conclusion in line 3 should contain both the minor term (S) and major term (P), but not the middle term (M).

D.    Standard Forms of Figures

1.     Our example syllogism above is a Figure 1 (AAA-1) out of a total of four Figures. To determine the figure of a syllogism we must have the proper distribution of the middle term.

2.     The following is a diagram  of the four figures:

 

3.     The following is a helpful diagram to determine the categorical figure.

        

 

4.    The EIO form example is an EIO-2.

1. No heroes are cowards.

2. Some soldiers are cowards.

3. Some soldiers are not heroes.

5.     The AEE form example is an AEE-4.

1. All kings are princes.

2. No princes are princesses.

3. No princesses are kings.

6.     The IAI form example is an IAI-3.

1. Some students are Freshmen.

2. All students are enrolled.

3. Some enrolled are Freshmen.

7.     Since there are four kinds of moods (A, E, I, O) and there are three propositions (Premise #1, #2, and a Conclusion) in a categorical syllogism, there are 64 possible moods (4 x 4 x 4 = 64). And since there are four different figures (Fig. 1, 2, 3, 4), there are 256 different forms of categorical syllogisms (4x 64 = 256). However, there are only 24 valid forms. This stresses the fact that there is a greater possibility for invalid arguments than valid.

 

IX.  LIST OF VALID SYLLOGISMS (24)

 

A.    AAA-1,  AAI-1,  AAI-3,  AAI-4,  AEE-2,  AEE-4,  AEO-2,  AEO-4,  AII-1,  AII-3,  AOO-2

B.    EAE-1,  EAE-2,  EAO-1,  EAO-2,  EAO-3,  EAO-4,  EIO-1,  EIO-2,  EIO-3,  EIO-4

C.    IAI-3,  IAI-4

D.    OAO-3

 

X.    LIST OF ALL VALID AND INVALID SYLLOGISMS (256)

 

A.    A - Combinations

 

A

 

 

Fig. 1

Fig. 2

Fig 3

Fig. 4

AAA-1: VALID

AAA-2: MID

AAA-3: MIN

AAA-4: MIN

AAE-1: MAJ-NEG

AAE-2: MID-NEG

AAE-3: MAJ-MIN-NEG

AAE-4: MIN-NEG

AAI-1: EXT

AAI-2: MID-EXT

AAI-3: EXT

AAI-4: EXT

AAO-1: MAJ-EXT-NEG

AAO-2: MID-EXT-NEG

AAO-3: MAJ-EXT-NEG

AAO-4: EXT-NEG

 

 

 

 

AEA-1: AFF

AEA-2: AFF

AEA-3: AFF

AEA-4: AFF

AEE-1: MAJ

AEE-2: VALID

AEE-3: MAJ

AEE-4: VALID

AEI-1: AFF-EXT

AEI-2: AFF-ECL

AEI-3: AFF-EXT

AEI-4: AFF-EXT

AEO-1: MAJ-EXT

AEO-2: EXT

AEO-3: MAJ-EXT

AEO-4: EXT

 

 

 

 

AIA-1: MIN

AIA-2: MID-MIN

AIA-3: MIN

AIA-4: MID-MIN

AIE-1: MAJ-MIN-NEG

AIE-2: MID-MIN-NEG

AIE-3: MAJ-MIN-NEG

AIE-4: MID-MIN-NEG

AII-1: VALID

AII-2: MID

AII-3: VALID

AII-4: MID

AIO-1: MAJ-NEG

AIO-2: MID-NEG

AIO-3: MAJ-NEG

AIO-4: MID-NEG

 

 

 

 

AOA-1: AFF-MIN

AOA-2: AFF-MIN

AOA-3: AFF

AOA-4: AFF-MID

AOE-1: MAJ-MIN

AOE-2: MIN

AOE-3: MAJ

AOE-4: MID

AOI-1: AFF

AOI-2: AFF

AOI-3: AFF

AOI-4: AFF-MID

AOO-1: MAJ

AOO-2: VALID

AOO-3: MAJ

AOO-4: MID

 

B.    E - Combinations

 

E

 

 

Fig. 1

Fig. 2

Fig 3

Fig. 4

EAA-1: AFF

EAA-2: AFF

EAA-3: AFF-MIN

EAA-4: AFF-MIN

EAE - VALID

EAE-2: VALID

EAE-3: MIN

EAE-4: MIN

EAI-1: AFF-EXT

EAI-2: AFF-ECL

EAI-3: AFF-EXT

EAI-4: AFF-EXT

EAO-1: EXT

EAO-2: EXT

EAO-3: EXT

EAO-4: EXT

 

 

 

 

EEA-1: ECL

EEA-2: AFF-ECL

EEA-3: AFF-ECL

EEA-4: AFF-ECL

EEE-1: ECL

EEE-2: ECL

EEE-3: ECL

EEE-4: ECL

EEI-1: AFF-ECL-EXT

EEI-2: AFF-ECL-EXT

EEI-3: AFF-ECL-EXT

EEI-4: AFF-ECL-EXT

EEO-1: ECL-EXT

EEO-2: ECL-EXT

EEO-3: ECL-EXT

EEO-4: ECL-EXT

 

 

 

 

EIA-1: AFF-MIN

EIA-2: AFF-MIN

EIA-3: AFF-MIN

EIA-4: AFF-MIN

EIE-1: MIN

EIE-2: MIN

EIE-3: MIN

EIE-4: MIN

EII-1: AFF

EII-2: AFF

EII-3: AFF

EII-4: AFF

EIO-1: VALID

EIO-2: VALID

EIO-3: VALID

EIO-4: VALID

 

 

 

 

EOA-1: AFF-ECL-MIN

EOA-2: AFF-MAJ-MIN

EOA-3: AFF-ECL

EOA-4: AFF-ECL

EOE-1: ECL-MIN

EOE-2: ECL-MIN

EOE-3: ECL

EOE-4: ECL

EOI-1: AFF-ECL

EOI-2: AFF-ECL

EOI-3: AFF-ECL

EOI-4: AFF-ECL

EOO-1: ECL

EOO-2: ECL

EOO-3: ECL

EOO-4: ECL

 

C.    I - Combinations

 

I

 

 

Fig. 1

Fig. 2

Fig 3

Fig. 4

IAA-1: MID

IAA-2: MID

IAA-3: MIN

IAA-4: MIN

IAE-1: MID-MAJ-NEG

IAE-2: MID-MAJ-NEG

IAE-3: MAJ-MIN-NEG

IAE-4: MAJ-MIN-NEG

IAI-1: MID

IAI-2: MID

IAI-3: VALID

IAI-4: VALID

IAO-1: MID-MAJ-NEG

IAO-2: MID-MAJ-NEG

IAO-3: MAJ-NEG

IAO-4: MAJ-NEG

 

 

 

 

IEA-1: AFF

IEA-2: AFF

IEA-3: AFF

IEA-4: AFF

IEE-1: MAJ

IEE-2: MAJ

IEE-3: MAJ

IEE-4: MAJ

IEI-1: AFF

IEI-2: AFF

IEI-3: AFF

IEI-4: AFF

IEO-1: MAJ

IEO-2: MAJ

IEO-3: MAJ

IEO-4: MAJ

 

 

 

 

IIA-1: MID-MIN

IIA-2: MID-MIN

IIA-3: MID-MIN

IIA-4: MID-MIN

IIE-1: MID-MAJ-MIN-NEG

IIE-2: MID-MAJ-MIN-NEG

IIE-3: MID-MAJ-MIN-NEG

IIE-4: MID-MAJ-MIN-NEG

III-1: MID

III-2: MID

III-3: MID

III-4: MID

IIO-1: MID-MIN-NEG

IIO-2: MID-MAJ-NEG

IIO-3: MID-MAJ-NEG

IIO-4: MID-MAJ-NEG

 

 

 

 

IOA-1: AFF-MIN

IOA-2: AFF-MIN

IOA-3: AFF-MID

IOA-4: AFF-MID

IOE-1: MAJ-MIN

IOE-2: MAJ-MIN

IOE-3: MID-MAJ

IOE-4: MID-MAJ

IOI-1: AFF

IOI-2: AFF

IOI-3: AFF-MID

IOI-4: AFF-MID

IOO-1: MAJ

IOO-2: MAJ

IOO-3: MID-MAJ

IOO-4: MID-MAJ

 

D.    O - Combinations

 

O

 

 

Fig. 1

Fig. 2

Fig 3

Fig. 4

OAA-1: AFF-MID

OAA-2: AFF

OAA-3: AFF-MIN

OAA-4: AFF-MIN

OAE-1: MID

OAE-2: MAJ

OAE-3: MIN

OAE-4: MAJ-MIN

OAI-1: AFF-MID

OAI-2: AFF

OAI-3: AFF

OAI-4: AFF

OAO-1: MID

OAO-2: MAJ

OAO-3: VALID

OAO-4: MAJ

 

 

 

 

OEA-1: AFF-ECL

OEA-2: AFF-ECL

OEA-3: AFF-ECL

OEA-4: AFF-ECL

OEE-1: ECL

OEE-2: ECL-MAJ

OEE-3: ECL

OEE-4: ECL-MAJ

OEI-1: AFF-ECL

OEI-2: AFF-ECL

OEI-3: AFF-ECL

OEI-4: AFF-ECL

OEO-1: ECL

OEO-2: ECL-MAJ

OEO-3: ECL

OEO-4: ECL-MAJ

 

 

 

 

OIA-1: AFF-MID-MIN

OIA-2: AFF-MIN

OIA-3: AFF-MID-MAJ

OIA-4: AFF-MIN

OIE-1: MID-MIN

OIE-2: MAJ-MIN

OIE-3: MID-MIN

OIE-4: MAJ-MIN

OII-1: AFF-MID

OII-2: AFF

OII-3: AFF-MID

OII-4: AFF

OIO-1: MID

OIO-2: MAJ

OIO-3: MID

OIO-4: MAJ

 

 

 

 

OOA-1: AFF-ECL-MIN

OOA-2: AFF-ECL-MIN

OOA-3: AFF-ECL-MID

OOA-4: AFF-ECL

OOE-1: ECL-MIN

OOE-2: ECL-MAJ-MIN

OOE-3: ECL-MID

OOE-4: ECL-MAJ

OOI-1: AFF-ECL

OOI-2: AFF-ECL

OOI-3: AFF-ECL

OOI-4: AFF-ECL

OOO-1: ECL

OOO-2: ECL-MAJ

OOO-3: ECL-MID

OOO-4: ECL-MAJ

 

XI.  SYLLOGISTIC FALLACIES

 

A.    1) AFF- Affirmative conclusion with a negative premise

1.     No E or O has A or I conclusion

B.    2) ECL- Exclusive negative premises

1.     No E or O in two premises

C.    3) MID- Undistributed middle term

1.     No connection by M

D.    4) MAJ- Illicit major term

1.     No connection with P

E.    5) MIN- Illicit minor term

1.     No connection with S

F.     6) NEG - Negative conclusion with affirmative premises (Clark)

1.     No A or I in two premises has E or O conclusion

G.    7) EXT- Existential affirmative from universal negative (Exception)

1.     Aristotelian logic consisted primarily of only 15 valid syllogisms.

a)     AAA-1,  AEE-2,  AEE-4,  AII-1,  AII-3,  AOO-2

b)    EAE-1,  EAE-2,  EIO-1,  EIO-2,  EIO-3,  EIO-4

c)     IAI-3,  IAI-4

d)    OAO-3

2.     The Existential (Conditional) Fallacy refers to two universal premises and a particular conclusion (9).

a)     AAI-1,  AAI-3,  AAI-4,  AEO-2,  AEO-4, 

b)    EAO-1,  EAO-2,  EAO-3,  EAO-4, 

3.     The above list would be valid if the critical term denotes actually existing things.

a)    Thus, if we are given an AAI-1 syllogism and the minor term is cats, then the syllogism is valid from the Aristotelian standpoint. But if the minor term is unicorns, then the syllogism is invalid. On the other hand, if the minor term is students who failed the exam and we are not certain if there are any such students, then the syllogism is conditionally valid. (Hurley)

4.     Those syllogisms which include only the Existential Fallacy (EXT) are for all intents and purposes considered valid.

H. Three Helpful Rules

        1. Rule 1: If one negative premise, then a negative conclusion (AFF).

        2. Rule 2: If two negatives, then invalid (ECL).

        3. Rule 3: If two affirmatives, then an affirmative conclusion (NEG).

 

XII. ENTHYMEMES

 

A.    Definition - An enthymeme (Grk enthumēma - thought, piece of reasoning) is argument or syllogism in which a statement, usually a premise, is missing. Enthymemes are used in everyday language. Scripture makes full use of enthymemes. Sometimes an enthymeme excludes a premise because it is generally assumed. Sometimes a statement is missing for emphasis. An enthymeme can also be used to slip in an invalid assumption.

B.    An enthymeme is discovered by turning the statement into syllogistic form. Note the following example: “Socrates is a man, therefore Socrates is mortal.”

1.     All men are mortal - missing premise

2.     Socrates is a man

3.     Socrates is mortal

C.    “Venus completes its orbit in less time than the Earth, because Venus is closer to the sun.”

1.     All planets closer to the sun complete their orbit in less time than the Earth.

2.     Venus is closer to the sun.

3.     Venus completes its orbit in less time than the Earth.

D.    Romans 5:12 Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned.

1.     All those who sin will  die

2.     All men sinned

3.     All men will die

E.    Romans 8:1 Therefore there is now no condemnation for those who are in Christ Jesus

1.     No one condemned is one who is in Christ

2.     Believers are in Christ

3.     No believer is one who is condemned) (EAE-2)

 

XIII.       SORITES

 

A.    Definition - A sorites (Grk. sōros - heap or quantity) is a chain of syllogisms in which the conclusion (sometimes missing) of a syllogism is the premise of the following syllogism(s). Note: Concerning sorites, the premises are often switched and can be juggled to the proper form. Note the following example:

1.     All bloodhounds are dogs.

2.     All dogs are mammals.

3.     (All bloodhounds are mammal) (AAA-1) - missing conclusion

4.     No fish are mammals.

5.     (Therefore, no fish are bloodhounds) (AEE-2)

A.    Here is a puzzle sorites for fun

1.     (1) Babies are illogical;

2.     (2) Nobody is despised who can manage a crocodile;

3.     (3) Illogical persons are despised.

---

4.     (3) Illogical persons are despised.

5.     (1) Babies are illogical;

6.     (All babies are despised) (AAA-1)

7.     (2) Nobody is despised who can manage a crocodile;

8.     (No one who can manage a crocodile is a baby) (AEE-4)

B.    Romans 8:30 and these whom He predestined, He also called; and these whom He called, He also justified; and these whom He justified, He also glorified.

1.     All who are predestined are called

2.     All who are called are justified

3.     (All who are predestined are justified)

4.     All who are justified are glorified

5.     (All who predestined are glorified)

C.    Luke 5:21 The scribes and the Pharisees began to reason, saying, "Who is this man who speaks blasphemies? Who can forgive sins, but God alone?"

1.     All who forgive sins are equal with God

2.     Jesus claimed to forgive sins

3.     (Jesus claimed to be equal with God) (AAA-1)

4.     All who claim to be equal with God are blasphemers

5.     (Jesus is a blasphemer) (AAA-1)

 

XIV.       RULES OF INFERENCE

 

A.    Definition of Inference:

1.     It is the logical connection of one proposition that follows (is inferred) from another.

2.     It is the act of drawing a valid conclusion based on premises in standard form, according to rules, and often expressed in conditional statements.

 

B.    Rules of Inference

 

1.     Modus Ponens (MP)

 

a)    It is called “Modus Ponens” (which means the “mode of positing”) because the second premise posits (i.e., sets down as fact) the antecedent of the conditional (first) premise. (The Power of Logic)

b)    It is in “conditional” form (if…then). “If” is the antecedent and “then” is consequent. “If it is raining (antecedent), then the ground is wet (consequent).”

c)     Stated form:  If p then q, p, therefore q.

d)    Symbolic styles:

 

(Power of Logic)      (Hurley)               (Craig)

      p → q                   p É q                1. P → Q

      p                            p____               2. P            

                                                                 \ q                            q                         3. Q       

 

e)     Ex. #1

1. (Premise #1)  -  If it is raining (p), then the ground is wet (q).

2. (Premise #2)  -  It is raining (p).

3. (Conclusion)  -  So, the ground is wet (q).

f)     Ex. #2 (converted to a categorical syllogism)

“If Socrates is a man, then Socrates is mortal.”

1. (All men are mortal - enthymeme)

2. Socrates is a man.

3. Socrates is mortal.

g)     Ex. #3

1. If the solution turns blue litmus paper red, then the solution contains acid.

2. The solution turns blue litmus paper red.

3. The solution contains acid.

h)    Ex. #4 (Premises can interchange)

1. Ben is a rat.

2. If Ben is a rat, then Ben is a mammal.

3. Ben is a mammal.

i)      Ex. #5 (Stylistic variants)

(“If it is raining (antecedent), then the ground is wet (consequent)”)

1. Given that it is raining, the ground is wet. (antecedent)

2. Assuming that it is raining, the ground is wet. (antecedent)

3. The ground is wet if it is raining. (antecedent)

4. The ground is wet given that it is raining. (antecedent)

5. The ground is wet assuming that it is raining. (antecedent)

6. It is raining only if the ground is wet. (consequent)

j)     Ex. #6 (Jn 8:31)

1. If you continue in My word, then you are truly disciples of Mine.

2. You continue in My word.

3. Then you are truly disciples of Mine.

k)    Ex. #7 (1Jn 1:9)

1. If we confess our sins, He is faithful and righteous to forgive us.

2. We confess our sins.

3. He is faithful and righteous to forgive us.

l)      Ex. #8 (Le 11:44; 1Pe 1:16)

 

1. If God is holy, then men must be holy.       1. If God exists, then objective morals exist.

2. God is holy                                                       2. God exists.

3. Men must be holy.                                          3. Objective morals exist.

 

2.     Modus Tollens (MT)

 

a)    Modus tollens means the mode or way of removing. The argument form gets its name from the second premise [~q], which denies (removes the truth of) the consequent of the first premise [q]. (The Power of Logic)

b)    Stated form:  If p then q, not q, therefore not p.

c)     The symbol ~ (tilde) stands for “not.”

d)    Symbolic styles:

 

(Power of Logic)     (Hurley)                (Craig)

      p → q                   p É q                 1. P → Q

    ~q                          ~q____              2. ~Q            

                                                                \ ~p                          ~p                       3. ~P        

 

e)     Ex. #1

1. If it is raining (p), then the ground is wet (q).

2. The ground is not wet (~q).

3. It is not raining (~p).

f)     Ex. #2 (converted to a categorical syllogism)

 “If Socrates is an angel, then Socrates is immortal.”

                                                             1. (All angels are immortal - enthymeme)

2. No Socrates is immortal. (Socrates is not immortal)

3. No Socrates is an angel. (Socrates is not an angel) (AEE-2)

g)     Ex. #3 (Jn 18:36)

1. If My kingdom were of this world, then My servants would fight.

2. My servants are not fighting.

3. My kingdom is not of this world.

h)    Ex. #4 (statements may include negatives; Also ~ ~ q is equivalent to q)

1. If God does not exit (~p), objective moral values do not exist (~q).

2. Objective moral values do exist (~ ~ q).

3. God exists (~ ~p).

 

3.     Fallacy: Affirming the Consequent

 

a)    Modus Tollens denies the consequent (~ q, not q) which is always valid. Affirming the consequent (q), results in an invalid conclusion. Therefore, it is a fallacy.

b)    Stated form:  If p then q, q, therefore p. (invalid)

c)     Symbolic styles:

 

(Power of Logic)      (Hurley)               (Craig)

      p → q                   p É q                 1. P → Q

     q                           q____                2. Q            

                                                                 \ p                           p                         3. P       

 

d)    Ex. #1

1. If it is raining (p), then the ground is wet (q).

2. The ground is wet (q).

3. It is raining (p). (A sprinkler could be on.)

e)     Ex. #2

1. If Fred is eating eggs, then he is having breakfast.

2. Fred is having breakfast.

3. Fred is eating eggs. (Fred could be eating pancakes.)

f)     Ex. #3

1. If evolution were true, we would expect to see similarities in DNA of all organisms on earth.

2. We do see similarities in DNA of all organisms on earth.

3. Therefore, evolution is true

Explanation: The evolutionist making such an argument has failed to recognize that creationists would also expect to see similarities in DNA of all organisms, since the original kinds were made by the same Creator. (Answers in Genesis).

 

4.     Fallacy: Denying the Antecedent

 

a)    Modus Ponens affirms the antecedent (p) which is always valid. Denying the antecedent (~p, not p) results in an invalid conclusion. Therefore, it is a fallacy.

b)    Stated form:  If p then q, not p, therefore not q. (invalid)

c)     Symbolic styles:

 

(Power of Logic)     (Hurley)                (Craig)

      p → q                   p É q                 1. P → Q

    ~p                          ~p                        2. ~P            

                                                                \ ~q                         ~q                        3. ~Q  

    

d)    Ex. #1

1. If it is raining (p), then the ground is wet (q).

2. It is not raining (~p).

3. The ground is not wet (~q). (The ground could be soaked but it may have stopped raining.)

e)     Ex. #2

1. If lemons are red, then lemons have a color.

2. Lemons are not red.

3. Lemons do not have color.

f)     Ex. #3 (Jn 11:21 - Martha’s comment was invalid)

1. If Jesus had come to Bethany sooner, Lazarus would be alive.

2. Jesus did not come to Bethany sooner.

3. Lazarus was not alive. (But Jesus did not intend to keep Lazarus alive, Jn 11:6)

 

5.     Hypothetical Syllogism (HS)

 

a)    Hypothetical Syllogism is a syllogism having a conditional statement for one or both of its premises (Also expresses as a sorites)

b)    Stated form:  If p then q, if q then r, therefore if p then r.

c)     Symbolic styles:

 

(Power of Logic)     (Hurley)                (Craig)

      p → q                   p É  q                1. P → Q

      q → r                   q É  r                  2. Q → R

  \ p → r                   p É  r                 3. P → R

 

d)    Ex. #1

1. If it is raining (p), then the ground is wet (q).

2. If the ground is wet (q), then Fred will wear his boots (r)

3. If it is raining (p), then Fred will wear his boots (r)

e)     Ex. #2 (Ro 8:29-30; can be converted into capital letters and symbols)

1. If believers are predestined (P), then they are called (C).

2. If they are called (C), then they are justified (J).

3. If they are justified (J), then they are glorified (G).

4. If believers are predestined (P), then they are glorified (G).

5. (Proof) P → C, C → J, J → G, \ P → G      

f)     Ex. #3

1. Babies (B) are illogical (I).

2. Nobody is despised (~D) who can manage a crocodile (M).

3. Illogical (I) persons are despised (D).

4. (Proof ) B → I, I → D, ~D → M (D → ~M) \ B → ~M           

 

6.     Disjunctive Syllogism (DS)

 

a)    Disjunctive Syllogism is a syllogism having a disjunctive statement (i.e., an ‘‘either . . . or . . .’’ statement) for one of its premises.

b)    Stated form:   Either p or q, not p, therefore q. (Also not q, therefore p)

c)     The symbol Ú (wedge or vee) stands for “or.”

d)    Symbolic styles:

(Power of Logic)     (Hurley)                (Craig)

      p Ú q                    p Ú  q                 1. P Ú Q

    ~p                        ~p                          2. ~P

 \ q                          q                           3. Q

 

e)     Ex. #1

1. Either it is raining (p) or the sprinkler is on (q).

2. It is not raining (~p).

3. The sprinkler is on (q).

f)     Ex. #2

1. Either Jesus was a liar or Jesus was Lord.

2. Jesus was not a liar.

3. Jesus is Lord.

g)     Ex. #3 (Ga 1:19a)

1. Either I am trying to please men or God.

2. I am not trying to please men.

3. Therefore, I am trying to please God.

 

7.     Constructive Dilemma (CD)

 

a)    Constructive Dilemma combines both conditional and disjunctive statements to arrive at a secondary conditional conclusion.

b)    Stated form:   Either p or q, if p then r, if q then s, therefore, either r or s.

c)     The symbols · (dot) or & stands for “and.” Also ( ) (parentheses) are used to confine an argument in complex statements.

d)    Symbolic styles:

 

(Power of Logic)            (Hurley)                                   (Craig)

      p Ú q                 (p É r)  ·  (q É s)             1. (P → R) &  (Q → S)                            

      p → r                 p Ú q                                2. P Ú Q

      q → s                 r Ú s                                 3. R Ú S

 \ r Ú s

 

e)     Ex. #1  p Ú q, p → r,  q → s, \ r Ú s

1. Either it is raining (p) or the sprinkler is on (q).

2. If it is raining (p), then it costs nothing (r).

3. If the sprinkler is on (q), then there is a utility charge (s).

4. Either it costs nothing (r) or there is a utility charge (s).

f)     Ex. #2  p Ú q, p → r,  q → s, \ r Ú s

1. Either Jesus is Lord or He was a liar.

2. If Jesus is Lord, then He must be worshipped.

3. If Jesus was a liar, then Christianity is a hoax

3. Either Jesus must be worshipped or Christianity is a hoax.

g)     Ex. #3  (p É r)  ·  (q É s), p Ú q, \ r Ú s

1. If Jesus is Lord, then He must be worshipped, and if Jesus was a liar, then Christianity is a hoax

2. Either Jesus is Lord or He was a liar.

3. Either Jesus must be worshipped or Christianity is a hoax.

 

8.     Conjunction (Conj)

 

a)    Conjunction states that if p is true, and q is true, it follows, “p and q” is true.

b)    Stated form: p, q, therefore, “p and q.”

c)     Symbolic styles:

 

(Power of Logic)     (Hurley)         (Craig)

      p                           p                    1. P

      q                           q                    2. Q

 \ p · q                     p · q              3. P & Q

 

d)    Ex. #1

1. It is raining (p)

2. The sprinkler is on (q).

3. Therefore, It is raining (p) and the sprinkler is on (q).

e)     Ex. #2

1. Jesus possesses a divine nature (D).

2. Jesus possesses a human nature (H)

3. If Jesus is divine and human, then He is a mediator (M).

4. Therefore, Jesus is a mediator (M)

f)     Ex. #2 Proof

1. D

2. H

3. (D & H) → M                   . : M            (Proof)

                                                4. D & H (Conj,1,2)

                                                5. M (MP,3,4)

               

9.     Simplification (Simp)

 

a)    Simplification states that if “p and q” is true, it follows that, p is true (q would also be true).

b)    Stated form:  p and q” therefore, p.

c)     Symbolic styles:

 

(Power of Logic)     (Hurley)         (Craig)

       p · q                     p · q            1. P & Q

  \ p                           p                  2. P            

 

d)    Ex. #1

1. It is raining (p) and the sprinkler is on (q).

2. It is raining (p).

e)     The main usefulness of this rule is that if you have the premise P & Q and you need either P by itself or Q by itself to draw a conclusion, simplification can give it to you (Craig).

f)     Ex. # 2a

1. Moses (M) was a great prophet and the prophets (P) were rejected.

2. If the prophets (P) were rejected, then Christ (C) was rejected.

3. Therefore, Christ (C) was rejected

g)     Ex. # 2 (Proof)

1. M & P

2. P → C                . : C            (Proof)

3. P (SP,1)

4. C (MP,2,3)

 

10.  Addition (Add)

 

a)    Addition seems at first to be a strange rule of inference: It states that if P is true, then “P or Q” is also true. What needs to be kept in mind is this: in order for a disjunction to be true only one part of the disjunction has to be true. So if one knows that P is already true, it follows that “P or Q” is also true, no matter what Q is! (Craig).

b)    Stated form:  p, therefore, p or q.

c)     Symbolic styles:

 

(Power of Logic)     (Hurley)         (Craig)

       p                            p                     1. P

       p Ú q                     p Ú q             2. P Ú Q

 

d)    Ex. #1

1. It is raining (p)

2. Either it is raining (p) or the gods are crying (q).

e)     Ex. #2 (1Co 14:37)

1. Someone is a prophet (P).

2. If someone is a prophet (P) or spiritual (S), then someone understands (U) the Word.

Therefore, someone understand (U) the Word.

f)     Ex. #2 (Proof)

1. P

2. (P v S) → U                       . : U            (Proof)

3. P v S (Add, 1)

4. U (MP, 2,3)

 

11.  Absorption (Abs)

 

a)    This is a rule which one hardly ever uses but which nonetheless states a valid way of reasoning. The basic idea is that since P implies itself, it implies itself along with anything else it implies. (Craig)

b)    Symbolic styles:

 

(Power of Logic)     (Hurley)                    (Craig)

     p → q                   p É  q                    1. P

     p → (p · q)          p → (p · q)           2. P → (P & Q)

 

c)     Ex. #1

1. If it is raining (p), then you need your umbrella (q)

2. If it is raining (p), then it is raining (p) and you need your umbrella (q).

d)    Ex. #2

1. If believers obey the commands of Christ, then they are His disciples.

2. If believers obey the commands of Christ, then they obey the commands of Christ and they are His disciples.

e)     Ex. #3 (The main use for absorption will be in cases where you need to have P & Q in order to take a further step in the argument. For example:

1. If creation appears to have a design (d), then there is a Designer (D).

2. If creation appears to have a design (d) and there is a Designer (D), then living things do not evolve (~E).

3. Therefore, if creation appears to have a design (d), then living things do not evolve (~E).

f)     Ex. #3 (Proof)

1. d → D

2. (d & D) → ~E                   .: d → ~E            (Proof)

3. d → (d & D) (Abs, 1)

4. d → ~E  (HS, 3, 2)

 

XV. ATTITUDE OF LOGIC AND WISDOM (Jm 3:17)

 

A.      Pure motives

 

1.     Most Bible versions translate hagnos simply as, “pure” or “chaste.” Indeed that is a good translation.

2.     But along with the idea of chaste behavior (1Pe 3:2) is the idea of innocent or without intent to do wrong (2Co 7:11; 1Ti 5:22).

3.     In the context of Jam 3, where James is speaking of social behavior (13-18), the meaning lends itself to innocent and without intent to do wrong.

4.     Concerning logic or reason, one must be pure in motives. There must be no hidden agendas (from which fallacies can spring) but only have the person’s best interest in mind. There must not be deception or manipulation but only a desire to arrive at the truth. This perspective must be first (prōtos).

 

B.      Peaceable

 

1.     The Greek word is a derivative of peace (eirēnē) and refers to someone who is peaceable (eirēnikos).

2.     This would describe someone who is not given to emotional tirades in order to argue their position.

3.     Rather their even-keel disposition adds to their message because it does not force the listener to make a decision based on emotion.

4.     In order to be peaceful there must be agreement, especially agreement to the truth.

 

C.      Gentle

 

1.     The word “gentleness” (epieikēs) has evolved since its classical origins. However, it has not completely lost all of its original meaning. Such words as kind, forbearing, and considerate are likely synonyms.

2.     The classical meaning was closer to the root eikos which meant what is reasonable. It includes synonyms such as fitting, suitable, plausible, accommodating, and reasonable.

3.     It is the idea that one’s speech and actions are fitting and suitable, not off-the-wall. To interact and dialogue successfully with others, there must be a willing reasonableness as well as suitable responses (Pr 25:11).

4.     It is certainly not a “my way or the highway” attitude. Therefore, gentleness (such as in the N.T. - Phil 4:5; 1Ti 3:3) is gentle in its presentation of the truth.

 

D.      Reasonable

 

1.     The literal meaning for this word (eupeithēs) means easily (eu) persuaded (peithō).

2.     It does not mean naďve or simple but one who is congenial or open to reason.

3.     This is the only time this word is used in the Bible, though it is used in the Apocrypha.

4.     Perhaps it goes without saying that to the one who desires to be logical, he must be “able to reason.” We must know how to reason and how to present our position in a reasonable manner (Is 1:18; Ac 17:2, 17, 22, 28; 18:4). This also includes being willing and able to listen to reason (Pr 18:13).

5.     It is the opposite of being unapproachable, unwilling to listen, and closed-minded.

 

E.       Full of Mercy

 

1.     Perhaps this quality might not be seen as a characteristic of logic and reason. But after all, this is the wisdom that is from above.

2.     The ultimate goal of the Christian apologist is not to win an argument at all costs, but to win a convert.

3.     Mercy (eleos - mercy or pity) is showing compassion toward the shortcomings of others, not exposing them. “Full of” is the Greek word mestos and has the idea of going beyond what could or should be expected

4.     The one who ridicules the shortcomings of others will never win an argument nor win the confidence of another.

5.     Mercy is also a rule in logic, though not always followed, We are to be charitable to arguments that are not necessarily well-crafted or carry many implied premises.

 

F.       (Full of) Good Fruits

 

1.     Good fruits coincide with pure intentions. The wisdom from above seeks the benefit of another (pure intentions) and then carries it out (good fruits).

2.     The goal of Christian logic and reason is not necessarily to win an argument but to produce fruitful Christian lives.

 

G.      Unwavering (“impartial” KJV, NET, NIV)

 

1.     Adiakritos means to be impartial or without prejudice and favoritism.

2.     Prejudice and favoritism never find their way in logic and reason. Prejudice and favoritism cause decisions to be fallacious and biased. Prejudice and favoritism are not based on s or truth.

3.     Prejudice and favoritism are denounced in the Bible (Jm 2:1 cp. Ro 2:11; Ep 6:9).

 

H.      Without Hypocrisy

 

1.     Wisdom and logic is to be “without hypocrisy” (anupokritos - a = negative & hupokrisis = Greek theatrical mask, to answer on a stage, pretend or put on).

2.     It is one thing to discuss truth, logic, and reason but it is another to live up to the truth we know. Hypocrisy is saying one thing but doing another.

3.     The Christian is not only to know the truth but also to live it (Jm 1:22).

4.     Many philosophers who postulated their views never lived up to their own philosophies.

5.     To be without hypocrisy means to be sincere, so sincere that one lives the truth they promote.

 

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APOLOGETICS

 

“ON GUARD” HANDOUT - 01

“Why Does Anything at all Exist?”

(Book Chapter 3)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     “On Guard”

 

A.    Book written by William Lane Craig on defending your faith with reason and precision.

B.    DVD Companion: Pastor Bobby Conway (“One Minute Apologist”) interviews William Lane Craig about each chapter in the book.

 

II.    Definition of a Good Argument

 

A.    An argument is a series of statements (premises) leading to a conclusion (Craig).

B.    What is a good argument?

1.     The premises need to be true.

2.     The conclusion needs to follow from the premises by the rules of logic.

3.     The premises need to be more plausible than their opposites. (Craig)

C.    From our Logic Class

1.     An argument that follows the rules of logic is called a "valid" argument.

2.     An argument that is valid and its premises are true is called a "sound" argument.

 

III.  Leibniz’s Argument

 

1. Everything that exists has an explanation of its existence (either in the necessity of its own    nature or in an external cause.)

                2. If the universe has an explanation of its existence, that explanation is God.

                3. The universe exists.

                4. Therefore the universe has an explanation of its existence (AAA-1 - 1, 3)

                5. Therefore, that explanation is God (MP - 2, 4)

 

IV.  Suggested Additional Resources Handout - 01

 

A.    Debate: Atheism vs. Christianity (Zindler vs. Craig)

1.     Youtube: http://www.youtube.com/watch?v=qOQnzfZEmxc

B.    Lecture: “Intellectual Neutral”

1.     Youtube: http://www.youtube.com/watch?v=7u-Eqwfmns8

2.     Reasonable Faith Video: http://www.reasonablefaith.org/media/in-intellectual-neutral-johnson-ferry-baptist-church#

 

V.    Scripture

 

A.    God said to Moses, "I AM WHO I AM"; and He said, "Thus you shall say to the sons of Israel, 'I AM has sent me to you (Ex 3:14).

B.    Before the mountains were born Or You gave birth to the earth and the world, Even from everlasting to everlasting, You are God (Ps 90:2).

C.    Your throne is established from of old; You are from everlasting (Ps 93:2).

D.    Do you not know? Have you not heard? The Everlasting God, the LORD, the Creator of the ends of the earth Does not become weary or tired. His understanding is inscrutable (Is 40:28).

E.    You are My witnesses," declares the LORD, "And My servant whom I have chosen, So that you may know and believe Me And understand that I am He. Before Me there was no God formed, And there will be none after Me (Is 43:10).

F.    In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God

G.    Jesus said to them, "Truly, truly, I say to you, before Abraham was born, I am (Jn 8:58).

 

VI.  Map Argument

 

A.    At the end of most chapters you’ll find an argument map or outline of the case presented in that chapter. Let me explain how to use the argument map.

B.    The map has a “swim lane” format that exhibits my argument in the left-hand lane labeled “Pro.” The right-hand lane labeled “Con” exhibits the objections that might be raised by an opponent of the argument.

C.    The arrows moving back and forth across the lanes trace the various Pro and Con responses that might be given. These maps will help you to see the big picture. (Craig, On Guard)

 

 

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“ON GUARD” HANDOUT - 02

“Why Did the Universe Begin?”

(Book Chapter 4)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     Kalam Argument:

 

1.     Whatever begins to exist has a cause.

2.     The universe began to exist.

3.     Therefore, the universe has a cause. (AAA-1)

 

II.    Terms and Concepts

 

A.    Infinite regress - (Philosophy, Logic) is a causal relationship brought about by an infinite number of causes. In regard to cosmological causality, infinite regress avoids the contradiction of spontaneous generation, but results in the absurdity of never explaining a first cause.

B.    Mill’s (and Russell’s) Fallacy - John Stuart Mill. (1806-1873), wrote “if everything must have a cause, then God must have a cause.” Besides the absurdity of infinite regress, Mill and Russell made another fundamental error.

1.     [Mill] made a fundamental error in his definition of causality. He assumed that the law of causality is simply, “Everything must have a cause.” If indeed the law could be defined in this way, then Mills criticism would be just. But such is not the case. The law of causality does not require that everything have a cause, only that every effect must have a cause. An eternal object need not have a cause…What we must strive to do, then, is find something that is not an effect, something that has the power of being within itself, something that has existed from all eternity. It [is] obvious to the Christian that this something is God, whom orthodox Christians have historically described as self-existing, eternal, and independent of all things. He is not caused simply because he is not an effect. (Sproul, Defending Your Faith)

 

III.  Scripture

 

A.    In the beginning God created the heavens and the earth (Ge 1:1)

B.    And, "YOU, LORD, IN THE BEGINNING LAID THE FOUNDATION OF THE EARTH, AND THE HEAVENS ARE THE WORKS OF YOUR HANDS; THEY WILL PERISH, BUT YOU REMAIN; AND THEY ALL WILL BECOME OLD LIKE A GARMENT (Ps 102:25-26; He 1:10-11).

C.    For thus says the LORD, who created the heavens (He is the God who formed the earth and made it, He established it and did not create it a waste place, but formed it to be inhabited), "I am the LORD, and there is none else (Is 45:18).

D.    By faith we understand that the worlds were prepared by the word of God, so that what is seen was not made out of things which are visible (He 11:3).

E.    All things came into being through Him, and apart from Him nothing came into being that has come into being (Jn 1:1-3).

F.    For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities-- all things have been created through Him and for Him (Col 1:16).

 

IV.  Additional Resources to Handout - 02

 

A.    Debate: What is the Evidence for/against the Existence of God - 1 (Atkins vs. Craig, 1998)

1.     Youtube: http://www.youtube.com/watch?v=BGsFPR4QX0M

B.    Debate: What is the Evidence for/against the Existence of God - 2 (Atkins vs. Craig, 2011)

1.     Youtube: http://www.youtube.com/watch?v=Ssq-S5M8wsY

 

 

 

 

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“ON GUARD” HANDOUT - 03

“Why is the Universe Fine-tuned for Life?”

(Book Chapter 5)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     Fine-tuning Argument:

 

1.     The fine-tuning of the universe is due to either physical necessity, chance, or design.

2.     It is not due to physical necessity or chance.

3.     Therefore, it is due to design. (Disjunctive Syllogism - 1, 2)

 

II.    Explanation

 

A.    The three possible reasons why our universe is fine-tuned for life are:

1.     Physical necessity: The constants and quantities must have the values they do.

2.     Chance: The constants and quantities have the values they do simply by accident.

3.     Design: The constants and quantities were designed to have the values they do.

B.    If someone has a fourth alternative, he’s welcome to add it to the list, and then we’ll consider it when we come to premise 2. But there doesn’t seem to be another alternative to the three listed here. Note: A fourth alternative cannot simply be an alternative from imagination. It would have to be a premise supported by reason and evidence, not simply an assertion.

 

III.  Richard Dawkins' Objections

 

A.    Detractors of design sometimes object that on this hypothesis the Cosmic Designer Himself remains unexplained. This objection is what Richard Dawkins calls “the central argument of my book” The God Delusion. He summarizes his argument as follows:

1.     One of the greatest challenges to the human intellect has been to explain how the complex, improbable appearance of design in the universe arises.

2.     The natural temptation is to attribute the appearance of design to actual design itself.

3.     The temptation is a false one because the designer hypothesis immediately raises the larger problem of who designed the designer.

4.     The most ingenious and powerful explanation is Darwinian evolution by natural selection.

5.     We don’t have an equivalent explanation for physics.

6.     We should not give up the hope of a better explanation arising in physics, something as powerful as Darwinism is for biology.

7.     Therefore, God almost certainly does not exist (DRH - concluded this way to avoid the burden of proof).

 

B.    Fallacies

 

1.     Non Sequitur (Latin for "it does not follow") - Dawkins’ atheistic conclusion … doesn’t follow from the six previous statements even if we concede that each of them is true. There are no rules of logic that would permit such an inference. Dawkins’ argument is plainly invalid. Dawkins’ lack of philosophical depth is plainly on display here.

2.     False Premises 5, 6 - Step 5 refers to the cosmic fine-tuning that has been the focus of our discussion. Dawkins has nothing by way of explanation for it, and therefore the hope expressed in step 6 represents nothing more than the faith of a naturalist.

3.     False Premise 3- Dawkins’ claim here is that we are not justified in inferring design as the best explanation of the complex order of the universe because then a new problem arises: Who designed the designer? But, you don’t need to explain the explanation

4.     False Assumption on Complexity - Dawkins’ fundamental mistake lies in his assumption that a divine Designer is just as complex as the universe. That is plainly false. As a pure mind without a body, God is a remarkably simple entity. A mind (or soul) is not a physical object composed of parts….Dawkins has evidently confused a mind’s ideas, which may, indeed, be complex, with a mind itself, which is an incredibly simple entity.

 

IV.  Scripture on Fine-tuning of the Universe

 

A.    In the beginning God created the heavens and the earth (Ge 1:1).

B.    The earth was formless and void, and darkness was over the surface of the deep, and the Spirit of God was moving over the surface of the waters (Ge 1:2). cf. Creation week (Ge 1:3-31).

C.    "It is I who made the earth, and created man upon it. I stretched out the heavens with My hands And I ordained all their host (Is 45”12).

D.    Covering Yourself with light as with a cloak, Stretching out heaven like a tent curtain (Ps 104:2).

E.    Thus says the LORD, your Redeemer, and the one who formed you from the womb, "I, the LORD, am the maker of all things, Stretching out the heavens by Myself And spreading out the earth all alone,(Is 44:24).

F.    For thus says the LORD, who created the heavens (He is the God who formed the earth and made it, He established it and did not create it a waste place, but formed it to be inhabited), "I am the LORD, and there is none else (Is 45:18).

G.    "You alone are the LORD. You have made the heavens, The heaven of heavens with all their host, The earth and all that is on it, The seas and all that is in them. You give life to all of them And the heavenly host bows down before You (Neh 9:6).

 

V.    Scripture on Design

 

A.    For You formed my inward parts; You wove me in my mother's womb. 14 I will give thanks to You, for I am fearfully and wonderfully made; Wonderful are Your works, And my soul knows it very well. 15 My frame was not hidden from You, When I was made in secret, And skillfully wrought in the depths of the earth; 16 Your eyes have seen my unformed substance; And in Your book were all written The days that were ordained for me, When as yet there was not one of them (Psa 139:13-16).

B.    Then God said, "Let Us make man in Our image, according to Our likeness; and let them rule over the fish of the sea and over the birds of the sky and over the cattle and over all the earth, and over every creeping thing that creeps on the earth." 27 God created man in His own image, in the image of God He created him; male and female He created them (Ge 1:26-27).

C.    But now ask the beasts, and let them teach you; And the birds of the heavens, and let them tell you. 8 "Or speak to the earth, and let it teach you; And let the fish of the sea declare to you. 9 "Who among all these does not know That the hand of the LORD has done this, 10 In whose hand is the life of every living thing, And the breath of all mankind? 11 "Does not the ear test words, As the palate tastes its food? (Job 12:7-11).

 

VI.  Additional Resources to Handout - 03

 

A.    Debate: Viability of Intelligent Design (Ayala vs. Craig)

1.     Youtube: http://www.youtube.com/watch?v=mfylw5okAag  

 

 

 

 

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“ON GUARD” HANDOUT - 04

“Can We be Good without God?”

(Book Chapter 6)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     Moral Argument:

 

1. If God does not exist, objective moral values and duties do not exist.

2. Objective moral values and duties do exist.

3. Therefore, God exists. (Modus Tollens, 1, 2)

 

II.    Explanations

 

A.    What makes this argument so powerful is that people generally believe both premises. In a pluralistic age, students are scared to death of imposing their values on someone else. So premise 1 seems correct to them because of its implicit relativism. At the same time, certain values have been deeply instilled into them, such as tolerance, open-mindedness, and love. They think it’s objectively wrong to impose your values on someone else! So they’re deeply committed to premise 2 as well. (Craig, “On Guard”)

B.    There’s the distinction between being objective or subjective. By objective I mean “independent of people’s opinions.” By subjective I mean “dependent on people’s opinions.” So to say that there are objective moral values is to say that something is good or bad no matter what people think about it. Similarly, to say that we have objective moral duties is to say that certain actions are right or wrong for us regardless of what people think. (Craig, “On Guard”)

C.    As Darwin himself wrote in The Descent of Man, If … men were reared under precisely the same conditions as hive-bees, there can hardly be a doubt that our unmarried females would, like the worker-bees, think it a sacred duty to kill their brothers, and mothers would strive to kill their fertile daughters; and no one would think of interfering. (Craig, “On Guard”)

D.    Now it’s extremely important that we clearly understand the issue before us. I can almost guarantee that if you share this moral argument with unbelievers, someone will say indignantly, “Are you saying that all atheists are bad people?” They’ll think you are judgmental and intolerant. We need to help them see that this is a complete misunderstanding of the argument...Rather the question is: If God does not exist, do objective moral values and duties exist? The question is not about the necessity of belief in God for objective morality but about the necessity of the existence of God for objective morality. (Craig, “On Guard”)

E.    The Bible reports many good deeds done by pagans such as Darius (Dan. 6:25–28), the city clerk of Ephesus (Acts 19:35–41), the Roman military officers who protected Paul (Acts 23:10, 17–35), and the natives of Malta who befriended Paul and his shipmates (Acts 28:10). The fact that such people did good things, knowing they were ethically good, proves they had knowledge of God’s Law written in their hearts. Therefore if those people never come to trust in the true God, their good deeds will actually witness against them on the day of judgment. (MacArthur Ro 2:14-15)

 

III.  Scripture

 

A.    For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves, n that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them. (Ro 2:14-15)

B.    but we have renounced the things hidden because of shame, not walking in craftiness or adulterating the word of God, but by the manifestation of truth commending ourselves to every man's conscience in the sight of God. (2Co 4:2)

C.    For I know my transgressions, And my sin is ever before me… Behold, You desire truth in the innermost being, And in the hidden part You will make me know wisdom. (Ps 51:3, 6)

D.    by means of the hypocrisy of liars seared in their own conscience as with a branding iron. (1Ti 4:2)

 

IV.  Suggested Additional Resources - Handout - 04

 

A.    Debate: Goodness without God (Kurtz vs. Craig)

1.     Youtube: http://www.youtube.com/watch?v=8F6y_6fIjAY

B.    Lecture: “Can We be Good without God?”

1.     Youtube: http://www.youtube.com/watch?v=bZXj26oIA68

 

 

 

13. 

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“ON GUARD” HANDOUT - 05

“What about Suffering?”

(Book Chapter 7)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     Atheist Argument: It’s Logically Impossible For God And Suffering To Coexist

 

1. An all-loving, all-powerful God exists (L&P).

2. Suffering exists (S).

3. If God is all-powerful (P), He can create any world that He wants (C).

4. If God is all-loving (L), He prefers a world without suffering (WS)

5. Therefore, God does not exist.

 

6. If an all-loving, all-powerful God exists (L&P), then He can and prefers to create a world without suffering (C&WS). (SP, 3, 4; AD,1)

7. However suffering exists ~(C&WS) (Premise 2)

8. Therefore, an all-loving, all-powerful God does not exist ~(L&P) (MT, 2,6, This is a valid logical form but unsound in it premises)

 

II.    Rebuttal of Premise # 3. If God is all-powerful, He can create any world that He wants.

 

A.    If God created man with a free will, then man can sin and bring about suffering.

B.    It would be logically impossible for God to make someone do something freely.

C.    If God is always consistent with His nature and truth, then He cannot do something logically impossible.

 

III.  Rebuttal of Premise # 4. If God is all-loving, He prefers a world without suffering.

 

A.    God can and does have overriding purposes for allowing the suffering in the world.

B.    The overriding purposes would be God’s glory and power over suffering, God’s revelation of His love in Christ, man’s salvation, the believer’s sanctification, and understanding of good.

C.    Conclusion: God could not have created another world with as much good as, but less suffering than, this world, and God has good reasons for permitting the suffering that exists.

 

IV.  Scripture

 

A.    These things I have spoken to you, so that in Me you may have peace. In the world you have tribulation, but take courage; I have overcome the world.(Jn 16:33)

B.    And not only this, but we also exult in our tribulations, knowing that tribulation brings about perseverance; and perseverance, proven character; and proven character, hope; and hope does not disappoint, because the love of God has been poured out within our hearts through the Holy Spirit who was given to us. (Ro 5:3-5)

C.    After you have suffered for a little while, the God of all grace, who called you to His eternal glory in Christ, will Himself perfect, confirm, strengthen and establish you. (1Pe 5:10)

D.    For you have been called for this purpose, since Christ also suffered for you, leaving you an example for you to follow in His steps. (1Pe 2:21)

E.    Therefore we do not lose heart, but though our outer man is decaying, yet our inner man is being renewed day by day. For momentary, light affliction is producing for us an eternal weight of glory far beyond all comparison, while we look not at the things which are seen, but at the things which are not seen; for the things which are seen are temporal, but the things which are not seen are eternal. (2Co 4:16-18)

F.    As for you, you meant evil against me, but God meant it for good in order to bring about this present result, to preserve many people alive. (Ge 50:20)

G.    And we know that God causes all things to work together for good to those who love God, to those who are called according to His purpose. For those whom He foreknew, He also predestined to become conformed to the image of His Son, so that He would be the firstborn among many brethren. (Ro 8:28-29)

 

V.    Suggested Additional Resources - Handout - 05

 

A.    Debate: Do Suffering and Evil Disprove God? (Sinnot-Armstrong vs. Craig)

1.     Youtube: https://www.youtube.com/watch?v=n8A3Sdw2Eig

B.    Lecture: “Is There meaning in Evil and Suffering?” Craig

1.     Youtube: http://www.youtube.com/watch?v=bZXj26oIA68

 

 

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“ON GUARD” HANDOUT - 06

“Did Jesus Rise from the Dead?”

(Book Chapter 8&9)

Grace Bible Church, Gillette, Wyoming

Pastor Daryl Hilbert

 

I.     A CASE FOR JESUS’ RADICAL SELF-UNDERSTANDING

 

A.    Jesus Had a Divine-Human Self-Understanding.

 

1.     The worship of Jesus by monotheistic Jews as God incarnate within twenty years of His death requires an adequate cause to be found in Jesus’ own claims.

 

2.     Explicit Claims

 

a)    Messiah

 

(1)   The belief in the early church that Jesus was the Messiah requires an adequate cause.

(2)   Peter’s confession (Mark 8: 27– 30)

(3)   Jesus’ answer to John the Baptist (Matt. 11: 2-6; Luke 7: 19– 23)

(4)   Jesus’ triumphal entry (Mark 11: 1– 11; John 12: 12– 19)

(5)   Jesus’ action in the temple (Mark 11: 15– 17)

(6)   Jesus’ condemnation by the Sanhedrin (Mark 14: 61– 65)

(7)   Jesus’ crucifixion as “King of the Jews” (Mark 15: 26)

 

b)    2. The Son of God

 

(1)   Parable of the vineyard (Mark 12: 1– 9)

(2)   “No one knows the Father but the Son” (Matthew 11: 27)

(3)   “No one knows … not even the Son” (Mark 13: 32)

(4)   Jesus’ trial confession (Mark 14: 60– 64)

 

c)     3. The Son of Man

 

(1)   Jesus’ favorite title

(2)   Reference to the divine-human figure of Daniel 7 (Dan. 7: 13– 14)

(3)   Jesus’ trial confession (Mark 14: 60– 64)

 

3.     Implicit Claims

 

a)    Jesus’ preaching of the kingdom of God (Matt. 19: 28)

b)    Jesus’ authority

 

(1)   The content and style of Jesus’ teaching (Matt. 5: 31– 32)

(2)   “Truly, I say to you” (Mark 8: 12; 9: 1; etc.)

(3)   Jesus’ role as an exorcist (Luke 11: 20)

(4)   Jesus’ claim to forgive sins (Mark 2: 1– 12)

 

c)     Jesus’ miracles (Matt. 11: 4– 5)

d)    Jesus’ role as Judge (Luke 12: 8– 9)

 

II.    A CASE FOR THE HISTORICITY OF JESUS’ RESURRECTION

 

A.    Evidence To Be Explained

 

1.     Jesus’ empty tomb

 

a)    The historical reliability of the story of Jesus’ burial supports the empty tomb.

b)    The story of Jesus’ empty tomb is independently reported in very early sources.

c)     Mark’s story is simple and lacks legendary development (Mk 15:37-16:7).

d)    The tomb was discovered empty by women (Jn 20:11-18; Mt 28:9-10).

e)     The earliest Jewish response to the disciples presupposes the empty tomb.

 

2.     Various individuals and groups experienced the appearances of Jesus

 

a)    Paul’s list of eyewitnesses to Jesus’ resurrection appearances guarantees that such appearances occurred (1Co 15:5-8).

b)    The gospel accounts provide multiple, independent reports of postmortem appearances of Jesus.

On the day of Christ’s resurrection

(1)   Mary Magdalene (Jn 20:11-18)

(2)   The other women (Mt 28:9-10)

(3)   Disciples traveling to Emmaus (Lk 24:13-32)

(4)   Peter (Lk 24:33-35 cp. 1Co 15:5)

(5)   All the disciples except Thomas (Jn 20:19-25)

Later in the forty day interval

(6)  Thomas and all the disciples (Jn 20:26-31)

(7)  Disciples at Sea of Galilee (Jn 21:1-25) - Peter’s Commission

(8)  Disciples on mountain at Galilee (Mt 28:16-20) - Great Commission

Including Five hundred brethren (1Co 15:6)

(9)  James (1Co 15:7) - James’ Commission

(10) Disciples at Jerusalem (Lk 24:44-49; Ac 1:3-8) - Second Commission

c)     The resurrection appearances were physical, bodily appearances (Lk 24:39).

 

3.     The first disciples believed in Jesus’ resurrection

 

a)    Jews had no expectation of a Messiah who instead of triumphing over Israel’s enemies would be shamefully executed by them as a criminal.

b)    Jewish beliefs about the afterlife preclude anyone’s rising from the dead to glory and immortality before the resurrection at the end of the world (Mt 22:23; Mk 12:18; Lk 20:27; Ac 23:8).

 

B.    Explaining The Evidence

 

1.     Rival explanations do not fare well when assessed by the standard criteria for the best explanation, such as explanatory scope, explanatory power, plausibility, being contrived, disconfirmation by accepted beliefs, and outstripping its rivals in meeting these criteria.

a)    Conspiracy theory

b)    Apparent death theory

c)     Displaced body theory

d)    Hallucination theory

2.     Conclusion: The resurrection theory when judged by these same criteria emerges as the best explanation.

 

III.  Suggested Additional Resources - Handout - 06

 

A.    Debate: Resurrection (Spong vs. Craig)

1.     Youtube: https://www.youtube.com/watch?v=zsXzu4tcOTI