faith and science logic fall 2010

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A Question, revisited…

Given that all of us have a unique worldview, how can we establish a common truth?

Rephrased:Is there a common language or method shared by scientists and theologians by which we can objectively determine truth?

I propose the answer is …LOGIC and REASON

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BY DR. SCOTT R . FRANKLIN

A very briefintroduction to logic and reason

A presentation to the Faith and Science Seminar

MSCI 3101Fall 2010

G.K. Chesterton

Men have always one of two things: either a complete and conscious philosophy or the unconscious acceptance of the broken bits of some incomplete and often discredited philosophy…. Philosophy is merely thought that has been thought out.

Divine Warnings

See to it that no one takes you captive by philosophy and empty deceit, according to human tradition, according to the elemental spirits of the world, and not according to Christ.

Colossians 2:8

Has not God made foolish the wisdom of the world? For since, in the wisdom of God, the world did not know God through wisdom, it pleased God through the folly of what we preach to save those who believe.I Corinthians 1:20b-21

Goals of Logic and Reason

To make reliable “objective” judgmentsTo identify and justify “good arguments”To learn the formal principles of “accurate

thinking”To Eliminate fluid arguments:

“That sounds good to me” “That may be true for you but . . .” “Whatever you say, you seem to know” “It must be right since _________ said it”

Important Points to Consider

Logic is concerned with the validity of the argument, NOT the truth of the conclusion.

We study logic to structure and strengthen our arguments. Logic gives validity to what we believe to be true.

We do not prove our faith by logic.We do not claim that only the “logicians” can

reach right conclusions, but we do claim that the logical is stronger than the illogical.

Terms and Definitions

Statement

Argument

Claim or Conclusion

Premise

Data

Terms and Definitions

ValidAn argument is valid

if its premises necessarily lead to

its conclusion

Bad ArgumentA bad argument is any other kind of

argument.

SoundAn argument is sound

it is valid and you accept that all its premises are true.

Good Argument

A good, convincing argument is a sound

arguments.

Identifying the premises and conclusions

Science studies the natural. That is all we ask of it. if there is any fact or truth beyond nature, science knows nothing about it and it has nothing to say on the subject.

-Richard W. Metz, “Don’t Throw Crackpottery at Haunted Houses,” New York Times, 1 August 1996.


The New York Times reported on May 30, 2000, that some scientists were seeking a way to signal back in time. A critical reader responded thus:

It seems obvious to me that scientists in the future will never find a way to signal back in time. If they were to do so, wouldn’t we have heard from them by now?- Ken Grunstra, “Reaching Back in Time,” New York Times, June 6, 2000.


There can be no such thing as a first event, looked at from strictly physical perspective. If things had to begin . . . (a big bang?) the question is, “Why only then, why not earlier?” The answer has to be: “Conditions were not yet right.” What was it for “conditions to become right”? Something had to happen first (i.e., before the big bang). Thus there is always an event presupposed by any posited “first event.” The big bang, even if it is science and not mere “literary conception,” is only an interesting event.

- Lawrence Dewan, “Big Bang, If There Was One, Was No Big Deal,” New York Times, May 7, 1990


If God were willing to prevent evil, but unable to do so, he would be impotent; if he were able to prevent evil, but unwilling to do so, we would be malevolent. Evil can only exist if God is either unwilling or unable to prevent. There is evil. If God exists, he is neither impotent nor malevolent. Therefore, God does not exist.

The Symbolic Logic Approach

We let variables represent statements (etc.) and then use connectives that combine them into compound statements. Negation (not): Conjunction (and): Disjunction (or): Conditional (implies, if … then): Biconditional (equivalences):

Symbolic Logic (cont.)

Def: A truth table lists the “truth value” of a statement for all possible “truth values” of the various parts of a statement.

Negation Conjunction Disjunction Conditional Biconditional

Other Definitions

Def: The converse of the statement p q is q p.EX: Being a Christian implies that one has a generous spirit.p: One is a Christianq: One has a generous spiritConverse: If a person has a generous spirit then they must be a Christian.

Rules of Logic – Quickly Skim!!

Commutative: ; Associative: Distributive: Idempotent: ; Double Negation: DeMorgan’s Laws:

Contrapositive: (

Nine Rules of Inference

1. Modus Ponens (M.P.)p qp qEX: All men are mortal, Socrates is a man, therefore he is mortal.

2. Modus Tollens (M.T.)p q~q ~pEX: I Corinthians 15: 12 - 19

Note: Each line is a premise and the conclusion begins with

Modus Tollens ExampleI Cor. 15: 12-19

If no general resurrection, then Christ is not risen. If Christ is not risen, then (our preaching is vain,

your faith is vain, we are false witnesses, yet in sins, the dead have eternally perished)

But it is not the case that (our preaching is vain, your faith is vain, we are false witnesses, yet in sins, the dead have eternally perished). [Modus Tollens]

So it is not the case that Christ is not risen. [Modus Tollens]

So it is not the case that there is no general resurrection.

Therefore, there is a general resurrection.

Rules of Inference (cont.)

3. Hypothetical Syllogism (H.S.)p qq r p rEX: If I learn logic I will write better essays. If I write better essays I will make better grades. Therefore, if I learn logic I will make better grades.

Rules for Inference (cont.)

4. Disjunctive Syllogism (D.S.)p q~p qEX: Evolution [is] a theory universally accepted not because it can be proven by logically coherent evidence to be true, but because the only alternative, special creation, is clearly (??) incredible. (Watson, D.M.S., 1929. Adaptation. Nature 124:233. )

Rules for Inference (cont).

5. Constructive Dilemma (C.D.)(p q ) (r s)p r q sEX: The Argument (Descartes)(1) Either I am having deceptive thoughts (caused by an Evil Deceiver) or I am not. (2) If I am having deceptive thoughts (caused by an Evil Deceiver), then I exist.(3) If I am not having deceptive thoughts, then I exist.Therefore,(4) I exist.

Rules for Inference (cont.)

6. Absorption: p q p (p q)

7. Simplification:p q p

8. Conjunction:pq p q

9. Additionp p q

One Last Valid Proof Technique

Proof by Counterexample:

To “disprove” the implication: p q find a single example of p such that q is not true.EX: All camels have one hump.EX: All Christians live righteously.EX: Every irreversible chemical reaction dissipates heat. (i.e. are exothermic)

An Example

Verify the validity of the argument:If God were willing to prevent evil, but unable to do so, he would be impotent; if he were able to prevent evil, but unwilling to do so, we would be malevolent. Evil can only exist if God is either unwilling or unable to prevent. There is evil. If God exists, he is neither impotent nor malevolent. Therefore, God does not exist.

Statement Labeling

W: God is willing to prevent evilA: God is able to prevent evilI: God is impotentM: God is malevolentE: Evil existsG: God exists

Structure of the Argument

Is it valid?

To see why, look at a truth table…

What if God is unwilling, unable, not impotent, not malevolent and both God and Evil exist?

Structure of the Argument

Invalid argument

True

True

True

True

True

False

New Version

𝑻𝒉𝒊𝒔𝒐𝒏𝒆 𝒊𝒔 𝒗𝒂𝒍𝒊𝒅 ,𝒃𝒖𝒕 𝒊𝒔 𝒊𝒕 𝒔𝒐𝒖𝒏𝒅?

Fallacies

Def: A fallacy is an error in reasoning. More specifically, it is a type of argument that may seem to be correct but proves, upon examination, not to be so.

Three main categories Fallacies of Relevance Fallacies of Presumption Fallacies of Ambiguity

Fallacies of Relevance

When an argument relies on premises that are not relevant to its conclusion and that argument cannot possible establish its true, the fallacy committed is one of relevance

R1: The Argument from Ignorance:Something is true since it has never been proven false.


R2: The Appeal to Inappropriate Authority:when an appeal is made to parties having no legitimate claim to authority in the matter at hand.

R3: Argument Ad Hominem:fallacious attach in which the thrust is directed, not at a conclusion, but at the person who asserts or defends it.


R4: The Appeal to Emotion:an argument that replaces the evidence and rational argument with expressive language and devices to excite emotions

R5: The Appeal to Pitya special case of appeal to emotion in which feelings of altruism and mercy are appealed to

R6: The Appeal to Forceusing force to achieve a conclusion


R7: Irrelevant Conclusionwhen an argument purporting to establish a particular conclusion is instead directed to proving a different conclusion.

Fallacies of Presumption

Unwarranted “leaps” in logic are called fallacies of presumption

P1: Complex Questionasking a question in such a way as to presuppose the truth of some conclusion buried in that question Lawyer: The figures seem to indicate that your sales

increased as a result of these misleading advertisements. Is that correct?

Fallacies of Presumption

P2: Begging the questionto beg the question is to assume the truth of what one seeks to prove, in the effort to prove it. (One form is the circular arguments) Is there a God?

Yes.How do you know?Because the Bible says so.How do you know the Bible is correct?Because it was inspired by God.

Fallacies of Ambiguity

A1. Equivocationwhen we confuse several meanings of a word or phrase.

A2. Accentwhen a premise relies on word emphasis for specific meaning We should not speak ill of our friends


A3. Compositionreasoning that the attributes of a part of a whole must be attributes of the whole itself “…the universe is spherical in form…because all the

constituent parts of the universe, that is the sun, moon, and the planets appear in this form” – Nicolaus Copernicus, “The New Idea of the Universe”


A4. Division:arguing what is true of the whole must be true of its parts or arguing what is true of a collection of elements is true of each element. All dogs are carnivorous. Basenjis are dogs.

Therefore basenjis are carnivorous (OK) Dogs are frequently encountered in the streets.

Basenjis are dogs. Therefore, basenjis are frequently encountered in the streets (not OK)

faith and science logic fall 2010

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