How do I prove this argument valid?

@Protoman2050,

Hi Protoman, Smile

I am not really into syllogisms but I believe this one is circular, actually as near as I can understand it, its solid, but circular arguments are apparently a no no. We have some gifted people here in the realm of logic I am sure they will show you the error of your ways. Good luck!! Smile

@boagie,

boagie wrote:

Hi Protoman,

I am not really into syllogisms but I believe this one is circular, actually as near as I can understand it, its solid, but circular arguments are apparently a no no. We have some gifted people here in the realm of logic I am sure they will show you the error of your ways. Good luck!!

Circular? How? Biconditionals express equivalence, and they have rules of inference. As you said, I'll wait for a logician to get to this thread.

@Protoman2050,

In circular reasoning, "The definition comes first and then the supposed proof is based on that definition. This is proving something (at the end) by making logical deductions from premises that themselves contain the conclusion. Looping from the end to the beginning that way is called circular reasoning. Circular reasoning often sounds right, but it is invalid nonetheless. ... It is often hard to recognize reasoning as circular because the steps between the first and last may be many." {Logic and Literary Argument by Eric Rabkin}

@boagie,

First, your criteria for the proof's solution. Deductive elimination commonly goes by the name "constructive dilemma." Same concept, different name. Reductio ad absurdum is a different matter. That is (from what I can tell) an "indirect proof." Both are indeed inferences, but the Reductio ad absurdum is a little more complex, because it requires nesting an argument inside another argument. But still, a good question.

But Boagie makes a good point. Bi-Conditionals could be considered a tautologies if we examine them a bit closer. But for all intensive purposes, I'm looking only at the logical rules to extrapolate a comparison. A tautology inference states that for any P, PvP or P&P can be inferred. And for a Bi-Conditional, it is true as long as both components have the same truth value. A lot like a tautology as Boagie points out. But you also have a good point in that we must look only at the equivalence factor in a bi-Conditional because we must adhere to inferences. So actually, both you and Boagie are right? and further with really good perspectives on the same problem.

But to get to your proof.

There are a few problems though. If you want to use a constructive dilemma for your argument, you run into a problem setting up your argument when you are required to provide a disjunction (either, or) of the two antecedents of your existing conditionals. The only conditionals you can use are derived from equivalence of the bi-conditional. So you would need to provide, in your given argument before the proof, C v J (basically, I am a Christian or I have Jesus as my Savior). But that does not sound right, even though it could theoretically be done in the proof. You would in a sense need to contradict your faith to further the argument that you are indeed a Christian?oddly enough. And this is where the reductio comes in. This is also a rule which needs you to contradict your belief in order to affirm it. (i.e. ~P, then P by Indirect proof). The use of these inferences are problematic? but not impossible. But still, we want to solve the proof.

This may be a simpler way to solve your proof.

Gotta love Modus Ponens! Hope this helps.

@VideCorSpoon,

VideCorSpoon wrote:

First, your criteria for the proof's solution. Deductive elimination commonly goes by the name "constructive dilemma." Same concept, different name. Reductio ad absurdum is a different matter. That is (from what I can tell) an "indirect proof." Both are indeed inferences, but the Reductio ad absurdum is a little more complex, because it requires nesting an argument inside another argument. But still, a good question.

But Boagie makes a good point. Bi-Conditionals could be considered a tautologies if we examine them a bit closer. But for all intensive purposes, I'm looking only at the logical rules to extrapolate a comparison. A tautology inference states that for any P, PvP or P&P can be inferred. And for a Bi-Conditional, it is true as long as both components have the same truth value. A lot like a tautology as Boagie points out. But you also have a good point in that we must look only at the equivalence factor in a bi-Conditional because we must adhere to inferences. So actually, both you and Boagie are right? and further with really good perspectives on the same problem.

But to get to your proof.

There are a few problems though. If you want to use a constructive dilemma for your argument, you run into a problem setting up your argument when you are required to provide a disjunction (either, or) of the two antecedents of your existing conditionals. The only conditionals you can use are derived from equivalence of the bi-conditional. So you would need to provide, in your given argument before the proof, C v J (basically, I am a Christian or I have Jesus as my Savior). But that does not sound right, even though it could theoretically be done in the proof. You would in a sense need to contradict your faith to further the argument that you are indeed a Christian?oddly enough. And this is where the reductio comes in. This is also a rule which needs you to contradict your belief in order to affirm it. (i.e. ~P, then P by Indirect proof). The use of these inferences are problematic? but not impossible. But still, we want to solve the proof.

This may be a simpler way to solve your proof.

Gotta love Modus Ponens! Hope this helps.

That's so cool! But I'd love to see the RAA proof...that'd look interesting --I have no problem in denying my faith if it's in the course of a logical proof to prove said faith--, in both propositional form and plain English. As well as the RAA proof of this:

1. God is either unity or triune
2. If God was unity, He could not know Himself
3. God can know Himself
4. Therefore, He must be triune

Thanks!

@Protoman2050,

Protoman

Quote:

"I am a Christian iff I have Jesus as my Savior. I have Jesus as my Savior. Therefore, I am a Christian."

1. C<->J
2. J
3. :.C

Thanks!

Remove the irrelevant term Christian and you are left with what saves you. The Person Jesus

@Alan McDougall,

I think the argument is syllogistically stronger if you replace have with accept. The formal proof, however, ought to remain the same.

@hammersklavier,

Alan McDougall,

You separate the two terms "Christian" and "Jesus" from one another? Etymologically, they are essentially the same thing, just called by different names. Christ is the English translation of the Latin Christus (greek khristos) describing Jesus by the attributes that he possesses like "healer," the anointed," etc. Jesus is essentially the same thing? "savior" from the Greek Iesous translated from the Aramaic Yeshua (Jeshua).

Conceptually, I would think even by the same token you could not separate the two terms.

@VideCorSpoon,

Vide, according to your etymology, Joshua is a derivative of Yeshua. I usually hear messiah is the Aramaic for Greek khristos, that is, 'anointed one.' But since Christianity refers explicitly to Jesus' traditional name, acceptance of Christianity requires acceptance of Jesus (as the Son of God) and vice versa; other religions get around this problem by positing that Jesus was a spiritually superior person--prophet, avatar, bodhisattva--in whatever belief system said faith draws upon (although not the Son of God {but his divinity is theoretically accepted in Hinduism}).

@VideCorSpoon,

VideCorSpoon wrote:

But Boagie makes a good point. Bi-Conditionals could be considered a tautologies if we examine them a bit closer.

He does? Why?

1. Not all bi-conditionals are tautologies no matter how closely we examine them. For example, Obama is president iff Obama is commander in chief of the armed forces of the United States is a true bi-conditional, but it is not a tautology.

2.And, tautologies are not circular. Tautologies are propositions. Arguments are circular. No tautology is an argument. Therefore, no tautology is circular.

3. And even if he knew what he was talking about, what would that have to do with the question?

@hammersklavier,

VideCorSpoon

Quote:

You separate the two terms "Christian" and "Jesus" from one another? Etymologically, they are essentially the same thing, just called by different names. Christ is the English translation of the Latin Christus (greek khristos) describing Jesus by the attributes that he possesses like "healer," the anointed," etc. Jesus is essentially the same thing? "savior" from the Greek Iesous translated from the Aramaic Yeshua (Jeshua).

I am familiar with Greek and Hebrew but make no claim of being an expert in the ancient forms of those languages

A Christian is a follower of Christ. Christ means Anointed One. The word Christianity is not synonymous with Christ. The name Jesus is also synonymous with Joshua.

Christianity is a religion and Christ is a person , the "Son of the Living God"

It is Christ Jesus that saves you, the person of Jesus not a religious way.

Jesus said I am the way the truth and the life. Note not his words but his person is the way to God. The I AM statement by Jesus reveals the truth about him , he is God clothed in a mortal body.

Messiah Messiah the anointed expected one of Judaism is not a saviour but a mighty warrior king.

Of course Jesus is the mighty worrier king of the gentiles as well as the Jews they just do not know it yet

@Alan McDougall,

Oh!! the language of logic

For those who might not be informed Smile

Tautologies and Contradictions

Tautologies

A truth table column which consists entirely of T's indicates a situation where the proposition is true no matter whether the individual propositions of which it is composed are true or false. The most simple example would be (p ∨ ?p).
p ?p (p ∨ ?p)
T F T
F T T

A proposition which is true independently of the truth or falsity of the atomic propositions from which it is composed is known as a tautology.

Contradictions

Similarly, a proposition which is false independently of the truth or falsity of the atomic propositions from which it is composed is known as a contradiction.

The simplest example of this would be (p ∧ ?p).
p ?p (p ∧ ?p)
T F F
F T F
[CENTER]Biconditional Statement
An "If-Then" Statement that is true in both directions.
Sample conditional statement: p q. This is read If p, then q AND If q then p. The biconditional statement is only true when both p and q have the same truth values.[/CENTER]

[CENTER][CENTER][/CENTER]

[CENTER][/CENTER]
[/CENTER]

@Protoman2050,

Protoman2050 wrote:

How do I prove this argument valid using reductio ad absurdum and disjunction elimination?

"I am a Christian iff I have Jesus as my Savior. I have Jesus as my Savior. Therefore, I am a Christian."

1. C<->J
2. J
3. :.C

Thanks!

Isn't there a problem with your major premise??? There is no generally accepted definition of a Christian so you need more than your own beliefs to define Christianity..And sometimes it is possible to believe Jesus came to save the world, and not alone Christians...

@Fido,

Hammersklavier,

I agree with what you say on etymological translations. Incidently, you may like this website Online Etymology Dictionary. I am a real big fan of etymology and I have to say that this website has been of great use to me for many years. You may like it as well if you have not come across it before.

On your point that Christianity requires in some way the acceptance of Jesus, I am in many cases inclined to agree with you. But that seems a bit problematic because Jesus is conceived differently in the same religion. The concept of the trinity for example is understood differently from Catholics as to Christians. For example, the trinity is understood by Catholics as three persons incorporated into a single being? ironically much like Spinoza asserted Ethics. Christians on the other hand delineate Jesus from God in substantial form. To tell the truth, I have never been crazy about the generalization "Christians" for Catholics, Christians, etc. but I suppose it has to be done for all intensive purposes.

As a side note? did you ever hear about Siddhartha Gautama being incorporated into Christian theology as a saint? I think there is a good chance that he may have actually been incorporated as a saint? it actually makes sense. Religious figures tend to be recycled (though that seems kinda harsh to say). The Virgin Mary (as Christians come to understand her) for example is actually traced back to the bronze age mother deity kubbaba which was then assimilated into Mycenaean culture as "kibbli," which then was incorporated into the Greek pantheon as "Artemis" (virgin goddess) and then picked up by the Romans as "Magnum Madder" (the great mother), etc.

Kennethamy,

Why not?

To address your first point, a tautology is P may replace or be replaced by PvP or P&P. This is logically bi-equivalent in translation. In bi-conditionals, they can (and notice I italicize "can" because I was highlighting how it "could" be seen as such if we "examine it a bit closer") be seen as tautologies because both replacement rules adhere to logical equivalence. Equivalence in so many words in the world of propositional logic states that two statements are equivalent if and only if they imply each other. The connective in each replacement rule implies equivalence which is shared between these two rules. If you do examine them, it can be seen. It all depends on how familiar you are with propositional logic and how far you can see the similarity. The bi-conditional you gave about Obama is for all intensive purposes a bi-conditional, but it can (notice the italics) be seen as such if we examine it further. No one said I had to be textbook all the time, and I believe I had a disclaimer in post #5 (P2, S3) as well.

To address your point number two, depends on how you look at it. Tautologiesa are as much replacement rules as propositions (which they are by the way? don't get me wrong). But I don't agree with the majority of your points though. Are all arguments circular? No. Are tautologies an argument? Yes. Why not? P=P || (P-->Q) & (Q -->P) or (P&Q)v(Q&P). Again? why not?

To address the third point? who said Boagie didn't know what he was talking about?

Alan McDougall,

I suppose we all have our own conceptions of Christ and Christianity. I'm Catholic? so I disagree with many of your statements on theological principles. But I am not that much of a ferverent Catholic so I am more or less impartial to the whole thing. But this is all about logic, not theology.

I don't agree with large parts of your summarizations of tautologies and contradictions. Truth tables (especially those with two variables? which I cannot really tell) are 4 variables deep? not 2 for a complete truth probability matrix. Also, it is usually best to separate the your variables from the proof. To be honest, I don't know how to make heads or tails of your truth tables and how they correlate with your explanations.

Fido,

In the realm of propositional logic, the sky can be green and unicorns could roam the earth devouring small kittens. "Christian" is Protoman's unique variable independent of what we may think.

@hammersklavier,

hammersklavier wrote:

{but his divinity is theoretically accepted in Hinduism}).

In Buddhism, too. He is thought of as a Bodhisattva.

@Didymos Thomas,

Let me try another approach

There is a room with two doors the one leads to death the other to freedom. The prisoner does not know which door leads to which destiny/

There are two wardens in the room with him. He is allowed only one question.

One warden is a liar the other truthful he does not know which

He is allowed only one question.

So he points to any one of the doors (The wrong one) and selects any warden at random and asks them a question.

Is the door I am pointing at the the door that leads to life.

If the answer is yes, he walks through the other door.

A negation lie cancels out truth

T F T
T T F

Or wrong =right

?

@Alan McDougall,

Alan McDougall wrote:

Let me try another approach

There is a room with two doors the one leads to death the other to freedom. The prisoner does not know which door leads to which destiny/

There are two wardens in the room with him. He is allowed only one question.

One warden is a liar the other truthful he does not know which

He is allowed only one question.

So he points to any one of the doors (The wrong one) and selects any warden at random and asks them a question.

Is the door I am pointing at the the door that leads to life.

If the answer is yes, he walks through the other door.

A negation lie cancels out truth

T F T
T T F

Or wrong =right

?

I will try to take care. But, after your post, I may not be able to do so.

@kennethamy,

kennethamy

Quote:

I will try to take care. But, after your post, I may not be able to do so.

Pray dear fellow why?:perplexed: :perplexed: :perplexed:

Christ = truth

Deceiver = lie

I should have stated that he (the prisoner) knew one warden was a liar

AND I SHOULD HAVE SAID IF THE PRISONER ASKES ANY WARDEN "WHAT WOULD THE OTHER WARDEN SAY IF THIS DOOR I AM POINTING AT IS THE ONE THAT LEADS TO LIFE?"

THE ANSWER IS ALWAYS THE OPPOSITE TO THE TRUTH DUE TO THE LIAR

If both warden were truthful, he does not know this

The prisoner points at one door and says Is the door I am pointing at the right one??

Answer yes The prisoner asked a truthful question to a truthful warden and got a truthful answer

T T T
T

If there is a lying warden then

He asks a truthful question to the liar who lies = F or

HE asks a truthful question to a truthful warden who gives him a false answer due to the liars influence

T T F
F

:perplexed:

T F T
T F

@Protoman2050,

Vide, Alan, et al: My point was to say that in the Christian Weltanschauung (which Calvin incidentally misspelled viz my avatar) the act of accepting Christ is what makes one a Christian. I think. Therefore, by saying (and truly believing, of course) "Jesus Christ died for my sins," one is inherently Christian.

This argument rests on whether one buys into the Christian mindset.

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