# Logic

### Judgment - The act of the mind "judgment" is simply affirming or denying something (not necessarily "judging" i.e., evaluating or criticizing) - The result, in thought, is a *proposition*. - The result, in language, is a *sentence*.

### Truth - Propositions are either true or false - Some propositions are unknown ("Trump is a two-term president") - Some propositions are meaningless ("'Twas brillig in the slithy toves") - Some propositions are paradoxical ("This statement is a lie") - But 99% are either true or false... the hard part is figuring out which is which!


### For example - "Trump won the election with Russia's help" - "Chickens are dinosaurs"

### Objective & subjective - Object / subject - It / who - That / me - World / self - Truth claim / reaction

### Subject & Predicate - The proposition is composed of two concepts: subject and predicate - The subject is what we are talking about - The predicate is anything we are affirming or denying about the subject

### Subject & Predicate - Example: God is love. (God=subject, love=predicate) - Example: "The Grand Canyon is the biggest, coolest hole in the ground in the cosmos." - Grand Canyon=Subject, the biggest, coolest hole in the ground in the cosmos=predicate - "God is love" is not the same as "Love is God" - "God is love" is *about* God (that he is a certain way); "Love is God" is about love (that it is divine).

### Kinds of Proposition 1. Categorical propositions ("apples are juicy" is about the *category* 'apple') 2. Compound propositions: hypothetical, disjunctive, or conjunctive

### Compound Propositions 1. Hypothetical: If P, then Q. "If apples are fruits, then they are not vegetables." 2. Disjunctive: P or Q. "Either apples are fruits or apples are vegetables." 3. Conjunctive: P and Q. "Apples are fruits and tomatoes are vegetables."

### Propositions and other speech acts 1. A part of speech is either a proposition or something else. 2. Propositions are simple or compound -- and that's it! 3. Everything else we do with language is not a proposition but something else: questions, exclamations, commands, etc: "Here's Jonny!", "Where's the beef?", "That back flip though!", "Get to your work!", "Ugh!" "Yay!"

### Truth - Truth is in propositions - Truth is not in terms (except by clarity) - Truth is not in arguments (except by the conclusion being true, which is a proposition, or the premises, which are propositions) - Logical truth is correspondance of thought to reality - Substantive truth is in God's mind, the world, reality - "Truth", faithfulness, 'emeth' is in people

### Simple Propositions 1. Universal affirmative (A) 2. Universal negative (E) 3. Particular affirmative (I) 4. Particular negative (O) ***A*** F ***I*** RMO -- I AFFIRM N ***E*** G ***O*** -- I NEGATE

### Quantifiers: "All", "some" or "none" - A: All S are P - I: Some S are P - E: No S are P (All S are *not* P) - O: Some S are not P

### Tricky "O" - Tricky: "Not all lawyers are crooks" - As in, no lawyers are actually crooks, or *some* are not crooks (but some are)? - Very trickY: "All lawyers are not crooks" (as in none are, or not all?)

### Examples - Turn to 156-7 - Not a proposition? - Simple proposition? - Compound proposition? - If simple, put in strict form

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# Jesus and Logic

### Reasoning - 'Man is a rational animal.' - 'Man' is gender inclusive, and concrete -- more inclusive than the sexist abstraction of 'humanity' which excludes almost all English speakers - 'Rational' means reasoning, wisdom, intuition, understanding, apprehension, etc. - Human reasoning begins with experience - Human reasoning knows particulars and universals - Syllogism: "3 proposition argument"

### Foundations of Syllogism (187-8) 1. Whatever is universally true of a subject must be true of everything contained in that subject 2. Whatever is universally false of a subject must be false of everything contained in that subject 3. Two things identical with one and the same third thing are identical with each other 4. Two things which are not identical with a third thing are not identical with each other

### Tautologies - Necessarily true - Self-evident - "Frogs are frogs" - "If the ball is round and red, then the ball is round" - No new information: "This candidate will be elected if there is sufficient voter turnout"; "X will be elected if X is elected" - "The team who can turn it around in the second half and convert possessions to touchdowns is going to walk away the winner" (The winner will win; the highest scorer will score the highest)

### Detecting arguments - Detect its presence (is there an argument here?) - Detect its conclusion - Detect its validity

### Conclusion indicators (192) - consequently - therefore - so - implies that - so you can see that - which demonstrates - as a result - for this reason

### Premise indicators - because - since - for - if we assume that - follows from - the reason that

### Explanations - He has shifty eyes (fact) because he is guilty (explanation) - He is absent (fact) because he is ill (explanation) - Is he guilty? Maybe. Not all shifty-eyed people are guilty. - Is he absent? Yes! Because he's ill? Maybe.

### Validity - 'Valid' means that the conclusion necessarily follows from the premises. - Again: validity means that *if* the premises are true *then the conclusion must be true* - Again: validity means that if the premises are true *it is impossible for the conclusion to be false*

### Validity Table | Premises T/F | Argument Valid | Argument Invalid | |-----------------------------|-----------------------------------|-----------------------------| | T | **Conclusion True** | Conclusion unknown | | F | Conclusion unknown | Conclusion unknown |

### False premises - If the argument is valid and the conclusion is *false*, then at least one premise must be false. - All evil spirits are birds. All evil sparrows are evil spirits. Therefore all sparrows are birds. (True conclusion, valid argument...) - The earth is a star. No stars are fish. The earth is not a fish.

### Invalid arguments - If an argument is invalid, the conclusion still may be true! - If an argument is invalid, all the premises may still be true! - If an argument is valid, all the premises and conclusion may still be false! - All dinosaurs are dead. Some presidents are dead. So some people are presidents. (True conclusion, invalid) - All pigs are purple. Purple things are immortal. Pigs are immortal. (Valid but all false) - The sky is blue. The grass is green. Therefore man is mortal. (All true, but invalid)

### Exercises (199) - The dullest exercises in the book!

### Willard, “Jesus the Logician” - Being disciples of Jesus includes submitting to him intellectually - The words "Jesus" and "Logician" feel disconnected - Yet to be his disciple, as scholars, requires thinking about him qua logician

### Theory and practice - Jesus did not develop logical theory, like Aristotle or Frege - But most thinkers don't do that - And thinkers who develop logical systems may or may not be more logical - Jesus did *use* logic - Jesus is a thinker (4) >... to see Jesus in a new light: to see him as doing intellectual work with the appropriate tools of logic, to see him as one who is both at home in and the master of such work.

### The Will to Be Logical >To be logical no doubt does require an understanding of what implication and contradiction are, as well as the ability to recognize their presence or absence in obvious cases. But it also requires the will to be logical, and then certain personal qualities that make it possible and actual... - Using logic requires intelligence (noticing implications and contradictions) - Using logic requires moral character (hypocrites, liars, thieves, murderers must avoid logic)

### Enthymeme - "His use of logic is always enthymemic" (2) - Enthymeme is a logical syllogism with one or more "suppressed premises", i.e., unstated - "If you want to be rich, you have to save." (If you want to be rich, you have to save. **You want to be rich.** **Therefore you have to save.**) - "Candide is a typical French novel; therefore it is vulgar." (**All typical French novels are vulgar**; Candide is a typical French novel; therefore Candide is vulgar.)

### Ritual Law Consistency 1. The disciples were walking through fields, stripping the grain and eating them. 2. The Pharisess accused them of breaking the law because violating ritual norm 3. Jesus points out that "there are conditions in which the ritual laws in question do not apply" 4. Jesus "brings up cases of this that the Pharisees already concede" (David, showbread; Priests, sabbath regulations)

### Ritual Law Consistency - Conclusion: > It logically follows, then, that one is not automatically guilty of wrongdoing or disobedience when they do not keep the ritual observances as dictated, in case there is some greater need that must be met. This is something the Pharisees have, by implication, already admitted by accepting the rightness in the two cases Jesus referred to.

### Ritual Law Consistency - Deeper issue: God's character and intention - Human ritual laws: >[Those who claim to practice the ritual law] are forced to choose between hypocrisy and open inconsistency, and he does sometimes use the word "hypocrisy" of them (e.g. Luke 13:15), implying that they knew they were being inconsistent and accepted it. In fact, the very idea of hypocrisy implies logical inconsistency. "They say, and do not" what their saying implies. (Matthew 23:2)

### Ritual Law Consistency >And legalism will always lead to inconsistency in life, if not hypocrisy, for it will eventuate in giving greater importance to rules than is compatible with the principles one espouses (to sacrifice, for example, than to compassion, in the case at hand), and also to an inconsistent practice of the rules themselves (e.g leading one's donkey to water on the sabbath, but refusing to have a human being healed of an 18­ year­long affliction, as in Luke 13:15­16).

### Resurrection >"Reductio ad absurdem" = reduction to absurdity. A form of disproof that accepts the opponent's thesis, derives an absurd conclusion (that is impossible or contradictory). If X leads to Y necessarily, and Y is false, then necessarily X is false.

### Resurrection 1. Sadducees reject resurrection. 2. Argue that if resurrection were true, then a women would have 7 husbands, which is absurd. 3. Therefore, there is no resurrection. 3. Jesus exposes the Sadducee assumption that the resurrection will be crude, exactly as the body is now. 4. Counterpoint: If God is the deity of Abraham, and God is not the deity of the dead, the Abraham is not dead. 5. That the dead *are* raised follows from the nature of God -- that God is the deity of the living.

### Messiah 1. Messiah is the son of David (accepted by his hearers) 2. David calls the Messiah "Lord" (Psalm 110) 3. Therefore, the Messiah is not *simply* the son of David (but also the son of Someone higher)

### Dismemberment > If your right eye makes you to stumble, tear it out, and throw it from you; for it is better for you that one of the parts of your body perish, than for your whole body to be thrown into hell (Matthew 5:29-30) - If righteousness is to be achieved by *not sinning*, then one should dismember oneself, for it is better to enter heaven without eyes or hands than to go, whole, to hell. - However, one should not dismember oneself. - Therefore, righteousness is not to be achieved by *not sinning* (but presumably, by repentence)

>C. S. Lewis and Francis Schaeffer. They all make relentless use of logic, and to great good effect. With none of these great teachers is it a matter of trusting logic instead of relying upon the Holy Spirit. Rather, they well knew, it is simply a matter of meeting the conditions along with which the Holy Spirit chooses to work

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