OK Christians. your chance. Convince me of God.

[The Grand Nudger]

Agreed, the argument I offered is invalid, but in what way does it differ from your own?

Ok the first argument I worded it like this.

Not A -> B
Not B
Therefore A.

Then I think you got confused with double negation,

So I re-wrote as

A -> B
Not B
Therefore Not A

Both of these are logically valid.

From other then God. The negation of that is "from God". The negation of "from God" is from "other then God".

Yours was written like this.

A -> B
B
Therefore A.

Which is invalid.

My confusion doesn't arise from negation or either of the two forms you are hoping to use in this argument Mystic (which is why I linked the wiki's I've been referring to...I do get things wrong often enough, you know, I try to check my own work..lol) My confusion arises in whether we're arguing that B is a necessary or a sufficient condition of A (and vice versa). Seeing as you applied the "if/then" and not "if and only if/then" - in addition to your later comments were looking at modus ponens, a valid form being

If A, then B
A
Therefore B

but not modus tollens, a valid form being

If A, then B
Not B
Therefore not A

These are the two arguments you are putting forward, correct? Am I mistaken in this, can you use modus tollens if the converse of the premise is not valid? If you're arguing sufficient condition (but not necessary condition) then the rule of inference (MP) set next to your own looks like this

Mystic-If A, then B
MP -If A, then B

So far so good.

Mystic-Not B
MP -A

Wtf just happened? The MP essentially states, If this statement is true(A), then it implies such and such (B) (that would be the line above), and then goes on the assert that the statement (A) is true. You're making some assertion about B at this point, why?

Mystic-Therefore Not A
MP- Therefore B

Ummm........again, MP seems to be drawing some conclusion about B, while you are drawing some conclusion about A

You seem to be attempting to use the rules of inference for neccesary condition in an argument (presumably) from sufficient condition. To leverage the MT wouldn't you be asserting necessary condition?

---

Ah, something I missed earlier, when you were explaining that you felt that b could be true even if a were not, but that a could not be true if b were not. Can't say I agree with you on that count, and that's part of establishing necessary condition.

[Mystic]

Rhythm, I never made such an argument. This was the first argument.

a) From God
b) Found in it much contradictions by people.

If not from God (not A), then there would be contradictions found by the people (b).
There isn't found any contradictions (not B)
Therefore not not A
Therefore A (double negation) It is from God

This is the 2nd argument.

a) not from God
b) found in it much contradictions by people.

If not from God (a), then there would be found in much contradictions by people (b).
There isn't found much contradictions by people (not b)
Therefore it is from God (not a)

What I am using is known as modus tollens.

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If you want a modus ponens version of the argument then it would go like this

If there is no contradictions found in the book, then it is from God
There is no contradictions found in the book.
Therefore it is from God.

That would be the logically equivalent in modus ponens. That would be a valid argument as well.

[The Grand Nudger]

Sorry, was falling asleep at the keyboard, had to get some shuteye. I love the whole sufficiency and necessity bit. I understand that the example I offered is invalid, and I understand the concept of transposition, you're explaining either to me does nothing to answer the questions I've asked you. After pouring over the last few pages I finally think I've figured out my disconnect. When you begin with the "not a implies b, not b therefore Implies not A" I mistakenly assumed you were arguing a sufficient condition with the rule of inference for necessary conditions (I'm used to seeing "if and only if" in conditionals of necessary condition, which was not present in the initial premise, and in a subsequent post you mentioned that A is sufficient for B- which further confused me as I thought you were discussing the premise and not transposition itself) In essence, I thought you were asking me to assume that the premise satisfied sufficient condition and then argued from necessary condition. I wasn't dissatisfied with the relative truth value of the premise, but the way that I thought the premise had been followed by the rule of inference for a different sort of premise - mea culpa.

Am I mistaken in this, does a premise which contains a necessary condition not have to be expressed as "if and only if", as opposed to sufficient conditions "if"?

To elaborate upon where I may be confusing myself.

If you get an A, you will pass the class - sufficient
If and only if you get an A, you will pass the class - necessary

If the narrative is from other than god, you will find contradictions - sufficient
If and only if the narrative is from other than god, you will find contradictions - necessary

(why do you keep explaining shit which my posts would demonstrate that I understand perfectly well, btw, rather than answering any of my questions about the way the premise is worded? It took me forever to realize where ourt disconnect was and it just so happens that it looks like this is precisely how we ended up with a disconnect in the first place. It would be difficult for me to have been blathering on about transposition, modus ponens, and modus tollens these past few posts..and identifying your arguments as some variant of them if I was not aware of this...so why explain that to me, rather than correct me on how if and iff are somehow equivalent - which is actually something I don't understand? When you translate the A->B as a necessary condition colloquially are you not required to translate it as if and only if? IOW, I'm not unclear on the subject of modus tollens, but leary that your argument -specifically as you worded it- is not modus tollens)

This conversation has been great btw, led me to a webcrawl that yielded an awesome article on conditionals and language and the issues the two create when combined.

[Mystic]

Am I mistaken in this, does a premise which contains a necessary condition not have to be expressed as "if and only if", as opposed to sufficient conditions "if"?

I had two classes that I learned logic in, and we never discussed necessary or sufficient conditions. Or if we did, I don't remember.

But "if and only if" is double implication.

It would mean A -> B and B -> A both.

If and only if , would be mean both A and B are sufficient and necessary conditions of each other.

In without double implication.

A -> B

B is a necessary condition for A, but A is not a required for B, rather is proves B if true, while B can be true without A being true.

If you get an A, you will pass the class - sufficient
If and only if you get an A, you will pass the class - necessary

No, If you get an A, you will pass the class, has both a necessary and sufficient clause.

Getting A is sufficient for passing the class, but passing the class is a necessary requirement for getting an A.

In the case of if and only if, statement, it's double implication.

It means these two sentences both.

IF you get an A, you will pass the class.
If you pass the class, you will get an A.

They are then both sufficient and necessary conditions of each other.

Each has to be true for the other to be true, and if one is true, then the other is true.

[The Grand Nudger]

See, and the explanation I was operating on for what constitutes a necesserary condition was

"A is necessary for B iff (“if and only if”) B can’t occur without A"

or

"it is impossible to have Y without X"

But if you don't require the -if and only if- for necessary conditions then what would the difference between a sufficient and a necessary condition be? How could you determine which rule of inference was the correct rule of inference to leverage?

For example, getting an a is sufficient for passing the class, but it is not necessary (you could get a c and pass)

But if getting an a is stated to be the only way to pass, that passing without an A was impossible....if and only if you get an A..that would be necessary condition.

As I keep enjoying this subject it occurs to me that only if would probably indicate a necessary conditionin colloquial better than if and only if. So maybe

"The narrative is from other than god -only if- one can find contradictions."

(as an amusing aside, the article that this conversation led me to touches upon the notion that the word "if" in english does not describe a uniform condition, leading to problems)

---

"In trying to show that there is an ambiguity infecting “if”-sentences in English, critics have focused on two doctrines they regard as mistaken: first, that there is a reciprocity between necessary and sufficient conditions, and, second, that “if p, q” and “p only if q” are equivalent ways of saying the same thing."
http://plato.stanford.edu/entries/necess...oForStaThe

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[Mystic]

No you can't think of that way, you have to work with what logicians means.

A ->B
A
Therefore B

Means A is sufficient for B being true.
While if B is true, it doesn't mean A is true.

A -> B
Not B
Therefore Not A
Means B is necessary for A to be true.
While if A is not true, it doesn't mean B is not true.

A->B

You have both a necessary condition (B) and sufficient condition (A).

If you do if only if,

Then you have A <->B

Which translates to

A->B
B->A

Then A is both sufficient and necessary condition for B, and B is both a sufficient and necessary condition for A.

This is called double implication.

---

Here is the verse from Quran:

أَفَلَا يَتَدَبَّرُونَ الْقُرْآنَ ۚ وَلَوْ كَانَ مِنْ عِنْدِ غَيْرِ اللَّهِ لَوَجَدُوا فِيهِ اخْتِلَافًا كَثِيرًا {82}
[Shakir 4:82] Do they not then meditate on the Quran? And if it were from any other than Allah, they would have found in it many a discrepancy.

[The Grand Nudger]

Um, Mystic, I most definitevly -can- think of it that way, demonstrated by the fact that I just did (and further demonstrating the problems with ambiguity in wording). What I just linked to you is from the Stanford Encyclopedia of Philosphy...so I feel pretty confident that I'm working with "what logicians mean"..................whatever the hell that means....

The two forms of argument you offered each have an unstated bit about A being a sufficient or necessary condition of B. Which form you're going to use depends on which way you're going, whether you're arguing that A is a sufficient condition (then modus ponens), or A is a necessary condition (then modus tollens). The rules of inference that follow depend upon this.

Looking at that verse it seems to me to be establishing a sufficient condition, not a necessary condition Mystic. If that were the case, then modus tollens is not the valid form of inference for such a premise. Which is what I've been trying to explain. I could, of course, be incorrect.

[Mystic]

Rhythm...

Modus Ponens makes use of sufficient condition. While Modus Tollens makes use of necessary condition.

Don't try to over-complicate it.

You can re-write every modul tollens in modus ponens and vice versa by re-arranging the premises.

[The Grand Nudger]

For...fucks.....sake Mystic. Look over my last few posts to see an elaborate and fairly exhaustive explanation of just that.

Does modus tollens use sufficient condition? Now, when you answer that question for yourself, look over my questions again (and your responses). I'm already aware that you can rewrite them. Take that verse, and use modus pollens on it for me. Rearranging the premise..you mean...you're going to rearrange the premise given in the Qu'ran.....so that you might use a modus tollens? Surely you can see why that might disappoint me? It's not a simple issue of rearrangement, afaik, it's an issue of there being no indication that it is a necessarry condition to begin with (and then no acknowledgement in the premise that such is the case)

[Mystic]

Looking at that verse it seems to me to be establishing a sufficient condition, not a necessary condition Mystic. If that were the case, then modus tollens is not the valid form of inference for such a premise. Which is what I've been trying to explain. I could, of course, be incorrect.

modus tollens is always valid with whatever A -> B is. It never is invalid. It may not produce a sound conclusion but it's always valid.

In the case of the verse there is two conditions,

If it's from other then God (sufficient condition)
Then they would have found there in much discrepancy (necessary condition).

Modus tollens makes muse of the necessary condition.