C.S. Lewis and Modus Tollens

[BigIdeaSeeker]

Jesus- liar, lunatic, lord, or LIBELED. Given the abundant inconsistencies in the gospels, the habits of ancient biographers, and what the early Christians had at stake, I'd definitely say the put words into Jesus' mouth. Yep, CS Lewis left one option out.

[Cashify]

Clearly the lord is omnipresent....but was banned by the 'authorities' around 1300 years ago from being present in lying or lunacy or being within those stricken by them. But Jesus' ministry was clearly prior to the 1300 year boundary stone, therefore he is the lord even if he was a lying lunatic.

[Cimbolic]

This is a great comment, Cashify !

[indignant99]

Their "hidden assumption" is that the OR's are XOR's rather than ordinary disjunctions. Thus, they have a premise (without a consequent). Then, they assume the TRUTH of the premise, axiomatically, which is just flat-out bogus.

[Cimbolic]

Yes! The OR's are really XOR's.

I am very glad you see that.

[brainouty]

Cimbolic, my love: going back to the Bible text behind the C.S. Lewis quip: Christ CLAIMED to be the Lord over 400 times. No offense, but only a bad scholar would not know that.

Now, either He is or is not. If untrue, He's lying or crazy. But if true...then it's a question of ADMITTING His Claim.

How one GETS to that admittance, is a separate process which the CS Lewis quip doesn't eliminate, imo.

So 3 variables, not merely P&Q. :)

Did that help?

[Cimbolic]

You always help me, beauty.

I love the way your mind works.

[brainouty]

And I yours. :)

[criggster]

"Also, the implication you give:

(~Li AND ~LU) > Lo

is equivalent to: ~Lo V ~(~Li AND ~LU)"

Absolutely not: If that were true, the implication I gave would be equivalent to

~(~Li AND ~LU) V ~Lo

by the commutativity of OR. Reversal of the equivalence you gave would imply the commutativity of implication.

[Cimbolic]

I didn't reverse an equivalent.

P -> Q

yields ~Q --> ~ P

the Modus Tollens.

[darktango78]

You didn't reverse it. What you did is is negate both terms of the disjunction when mapping from the implication, as opposed to just the antecedent.

[Cimbolic]

Thanks, darktango.

I believe they call the rule "Transposition".

[darktango78]

Hey Cimbolic.

Transposition is the reversal of the implication with the negation of the terms.

The identity I'm referring to is

P -> Q equivalent to ~P v Q.

In the statement criggster is reffering to you wrote

"(~Li AND ~LU) > Lo

is equivalent to: ~Lo V ~(~Li AND ~LU)"

You negated both terms of the disjunction as opposed to just what was the antecedent (the left hand side of the implication.)

[Cimbolic]

Heyya darktango,

We differ in this:

I say ~Q V P

You say ~P V Q

I say tomato you say tango. :)

[darktango78]

Hahaha... Well logic is not a matter of taste :p

If you check above, I gave you the reason why the equivalence you're using doesn't hold (namely the instance where P is false and Q is true.)

Also, just as back up, if you google "logical identities", the first hit is from Rutgers University. If you follow that link, this equivalence is listed in the table under "implication."

[Cimbolic]

OMG, I'm wrong !!!

P --> Q is equivalent to Q V ~P as you say.

Thank you for pointing it out, darktango!

Sorry to drive you crazy.

[darktango78]

Haha! No worries!

It's great having a discussion on propositional logic because most of the time, it breaks down to basics and you can really "see" it.

My hair's all there for now. I was just having really bad gklr flashbacks and thinking "no, not again!"

Not to draw a comparison, because you're a very reasonable guy :)

[Cimbolic]

I was having the same flashbacks !

[gogreen18]

i loved this nick! yay symbolic logic! :]]

[Cimbolic]

Glad you do, Laci !

A little Cimbolic logic. :)

[criggster]

The disjunction, Liar v Lunatic v Lord,

is logically equivalent to the implication (~Liar ^ ~Lunatic) > Lord

The logic is valid, it's just that the premises are false.

[Cimbolic]

I disagree.

Li V Lu V Lo

Is a simple statement, a string of OR statements. It is not an implication.

If any of the three statements is true, then the statement as a whole is true.

Phased as:

Either Li or Lu, or Lo

what is meant is:

Li or Lu, or else Lo

Which is equivalent to:

(Li V Lu) --> ~Lo

[Cimbolic]

Then

~ (Li V Lu) is asserted.

And falaciously,

~~ Lo is concluded

~~Lo = Lo

So, Lo is concluded.

Fallaciously.

[Cimbolic]

Also, the implication you give:

(~Li AND ~LU) > Lo

is equivalent to: ~Lo V ~(~Li AND ~LU)

which is equivalent to: ~Lo V Li V Lu

NOT to: Lo V Li V Lu

as you assert.

[darktango78]

Sorry Cimbolic, I haven't watched the video yet and was reading the comments first, but

criggster is right. Any implication can be rewritten (is logically equivalent to) a disjunction (an or.)

The implication A -> B is logically equivalent to the disjunction ~A v B.

So (~Liar ^ ~Lunatic) -> Lord is logically equivalent to

~(~Liar ^ ~Lunatic) v Lord

which in turn is equivalent to

Liar v Lunatic v Lord

I'll watch the video now and give you more feedback.

[Cimbolic]

Hi darktango.

Yes, any implication can be rewritten as a disjunction, but not the one you and criggster assert.

A --> B

is equivalent to: ~B V A

not to: ~A V B

Thanks for watching the video.

[darktango78]

No, no, no... You're making me pull my hair out :p

You can do a truth table and you'll see that your equivalence doesn't hold.

If A is false and B is true, the implication, logically, holds. But in this case, your formula ~B v A would be false.

[Cimbolic]

I know. I'm pulling my hair out too.

I will run the truth tables.

[criggster]

But you have such a beautiful head of hair! Don't ruin it!

[Cimbolic]

Hey, you guys were right about

P --> Q being Q V ~ P.

My error, sorry to drive you crazy !!!!

[Cimbolic]

LOL!

I forgot I shaved my head !

[darktango78]

Awesome. Feel free to PM me.

I watched the video and while the "re-writing" you use is not correct, you're right about it being a false trilema.

Essentially, Lewis's argument is valid (if the premises are true, the conclusion must be true), but it's just not sound (the premises are not true.)

[Cimbolic]

Criggster feels Lewis's argument is valid, too.

This is what makes this argument interesting to me. It is very strange.

I think there is a hidden "or else", i.e. an exclusive or (XOR) hidden in it.

[criggster]

Well there are two more possibilities I can think of: Jesus could have been a legend or could simply have been mistaken. I feel it is the latter.

Also, I don't think it has been conclusively demonstrated that he wasn't a lunatic or liar.

[Cimbolic]

Yes:

Possibly never existed.

Possibly was in error.

Those are hidden assumptions in argument.

I also agree with you on your latter point.

I have very high standards of proof.

Way beyond "preponderance of the evidence", which means 51%.

It's got to be at least "beyond a reasonable doubt". But even then, i wouldn't be satisfied.

[darktango78]

Right, the argument is:

Premise 1: A v B v C

Premise 2: ~A ^ ~B

Conclusion: C

In plain English, the argument is "at least one of these three things is true. It's not the first and it's not the second. The third must be true."

You can do the truth table again (this time with 8 possibilities) and see that A v B v C is equivalent to "~A ^ ~B --> C".

(continued.)

[darktango78]

(cont.)

An intuitive instance you can think of is this. Imagine there are three doors and I tell you, "the prize is behind one of these three doors. It's not behind door 1 and it's not behind door 2." You can conclude then that, if what I told you is true, then the prize MUST be behind door 3.

In the case of Lewis's trilema, while the argument is valid, you can attack the premises. Namely, there are more possibilities than just those three, and quite possibly Jesus WAS a lunatic or a liar.

[Cimbolic]

Exactly what criggster says.

I agree with you both.