## Sunday, February 19, 2006

### No One Responded to my Horrible Argument, Therefore I Must be Right

Dr. Zachary Moore has been trying for over a year now to understand the form of a transcendental argument. The form is simple, really. It is:

<> P-->Q
<> P
:.Q

This is basically noted in this book, this book, this book, as well as by philosophers who specialize on TAs, such as Genova, Chisholm, Strawson, et. al.

A while back Dr. Moore tried to show that Van Til committed a school boy fallacy -affirming the consequent. Here is the gist of his post:

Van Til's claim that, "The only "proof" of the Christian position is that unless its truth is presupposed there is no possibility of "proving" anything at all" should be translated like this:

"1. ~P-->~Q
2. Q
3. :. P" (Moore's translation of the above).

Moore's conclusion: "Aha! Again we see Van Til’s fallacy of Affirming the Consequent. Paul has tried to hide this fallacy, but the illusion doesn’t last."

Certainly this is valid, but Zach doesn't know how to translate arguments into proper form. An argument having the form "p unless q" has three equivalent propositions

p unless q
p if not-q
if not-q, then p

Consequently, "p unless q" is exactly equivalent to "if not-q, then p," and should be translated that way (cf. any text on logic). (Note, sometimes you can translate "p unless q" as "p v q," depending on context. But, this is a disjunct and so does not help Moore's formulation, anyway. Put differently, if we translate Van Til's statement into a disjunctive syllogism Moore still fails.)

So, we can see that Moore's formulation: ~p --> ~q, q, :. p is an improper translation. The proper translation would be ~q --> p. Then from here one could either go: ~p, :.q, or ~q, :. p.

Now, Dr. Moore is still trying to find problems with the formulation of TAG (Note that if he does then he finds problems with all the philosophers I mentioned above. Likely?).

Most recently, Dr. Moore attacks a friend of mine, Pastor Dustin Segers, and tries to show that Segers is another moron who affirms consequents. Moore takes something Segers writes and subjects it to Moorean analysis.

1) For X to be the case, Y has to be the case.
2) X is the case.
3) Therefore, Y is the case.

And Moore responds,

"Read that first premise to yourself slowly a few times. Does that seem strange to anyone? This is not the standard language used to make a conditional statement. The standard language would be:

"If X is the case, then Y is the case."

Well, part of learning logic is to be able to translate ordinary language into "standard language."

Moore than translates the above as:

1) If Y is the case, then X is the case.
2) X is the case.
3) Therefore, Y is the case.

And pats himself on the back, writing: "Now we can easily see that this argument takes the form of the logical fallacy Affirming the Consequent."

Moore's main beef is with what he calls Dustin's "for-has" language. Since Dustin said For X ... Y has... then Moore thought that gave him the right to translate the argument as affirming the consequent.

Well, Moore's post was silly and so I never bothered to respond.

But this caused Moore to gloat: "No presuppositionalists want to weigh in on this before it slips off the front page? Well, I guess I had it right, then."

Besides the argumentum ad ignorantium, Moore's attitude makes one laugh. Moore then bragged about his decimation of Dustin on John Loftus' blog. So I thought I would help the good doctor out. I simply said,

"Dustin said, For X to be the case Y *has* to be the case. This shows that Y was the necessary proposition. When translating a conditional proposition, you place the sufficient condition in the antecedent position and the necessary condition in the consequent position."

I also asked Moore to back up his translation from a logic text.

Moore's response was not to admit that he was wrong (which should give us pause when we argue with him, knowing that he's out to preserve himself and atheism, at all costs. Truth, whatever that is, takes the hindmost) but rather he said,

"If I'm wrong, show that I'm wrong. You're still doing nothing but sniping and complaining. Which is it- is X dependent on Y or is Y dependent on X? Show me the logic book that lets you construct a syllogism that way."

Again, when translating a hypothetical conditional the necessary proposition goes in the place of the consequent, Moore! Dustin's use of the phrase "has to be" should have been enough for Moore to translate it properly. That is, if Moore has a modicum of understanding about logic. Moore wants me to back this up?

Okay

Stanford Encyclopedia of Philosophy offers support. Here's a quote:

The front door is locked. In order to open it (in a normal, non-violent way) and get into the house, I must first use my key. A necessary condition of opening the door, without violence, then, is to use the key. So it seems true that

(i) If I opened the door, I used the key.

Can we use the truth-functional understanding of "if" to propose that the consequent of any conditional (in (i), the consequent is "I used the key") specifies a necessary condition for the truth of the antecedent (in (i), "I opened the door")? Many logic and critical thinking texts use just such an approach, and for convenience I call it "the standard theory" (see Blumberg 1976, pp. 133 - 4, Hintikka and Bachman 1991, p. 328 for examples of this approach).

The standard theory makes use of the fact that in classical logic, the truth-function "p ⊃ q" ("If p, q") is false only when p is true and q is false. The relation between "p" and "q" in this case is often referred to as material implication. On this account of "if p, q", if the conditional "p ⊃ q" is true, and p holds, then q also holds; likewise if q fails to be true, then p must also fail of truth (if the conditional as a whole is to be true). The standard theory thus claims that when the conditional "p ⊃ q" is true the truth of the consequent, "q", is necessary for the truth of the antecedent, "p", and the truth of the antecedent is in turn sufficient for the truth of the consequent. This relation between necessary and sufficient conditions matches the the formal equivalence between a conditional formula and its contrapositive ("~q ⊃ ~p" is the contrapositive of "p ⊃ q". Descending from talk of truth of statements to speaking about states of affairs, we can equally correctly say, on the standard theory, that using the key was necessary for opening the door."

Another source would be Wikipedia. Here's a quote: "The truth of the antecedent is a sufficient condition for the truth of the consequent, while the truth of the consequent is a necessary condition for the truth of the antecedent."

Another source would be from
the thinking shop (under the section, "tips for translating." As a side, notice that they have a section called "translating." When I used this word for translating for-has to if-then, Moore mocked me, saying: "I do think it's really funny to talk about "translating" English to English. Somehow "for-has" to "if-then" is "translating." You're a riot." Get that! Moore doesn't even know that that is what it is called. What a riot that guy is).

And so with that said, I think it is fitting to end with something Steve Hays said chestnuts (I'll just replace Loftus with Moore:

Thus far, the chief threat which Zachary Moore poses to the church is that Christian intellectuals will become cage fat from the yummy diet of intellectual junk food he’s been dishing up for our consumption.

We’ve never had it so easy. We no longer need to write original essays. We simply mouse over to his blog once a day, and he supplies us with all the honeyed corn mush we need to do a post of our own.

I’d advise my fellow bloggers not to become overly indolent from living off the fat of the land. Rather, we should squirrel away this bountiful summer’s harvest of warmed over chestnuts for the lean months to come. It’s just too good to last. Rationing is the only prudent policy. “Chestnuts roasting on an open fire…”

~Paul

1. It's not difficult to see that Segers has it right (with regard to logical form) by plugging some simple illustrative states-of-affairs into X and Y, e.g.:

X = Sam's thinking about his lunch
Y = Sam's thinking

(Note that I'm plugging states-of-affairs rather than propositions into X and Y because of the "is the case" locutions; the apostrophes in the above are possessive rather than abbreviative.)

It should be obvious that For X to be the case, Y has to be the case (i.e. For Sam to be thinking about his lunch, Sam has to be thinking) is equivalent to If X is the case, then Y is the case (i.e. If Sam is thinking about his lunch, then Sam is thinking) rather than If Y is the case, then X is the case (i.e. If Sam is thinking, then Sam is thinking about his lunch).

Actually, to be still more precise, the claim For X to be the case, Y has to be the case is better translated as Necessarily, if X is the case, then Y is the case (which captures the modality indicated by the phrase "has to be").

But in any event, Segers is not at all guilty of affirming the consequent.

This is Logic 101, guys. I'm afraid that Moore's criticisms of Segers, and the laudatory comments of his fellow bloggers, don't do much for their philosophical credibility.

2. This is the first time I've seen you use this form:

<> P-->Q
<> P
:.Q

How is this written in natural language?

3. Zach, that's not the first time you've seen *the form*

For *the form* is modus ponens, as you admited I wrote elsewhere.

What form did you think the above was? Milis Finkins? I know, they look alike :-)

Anyway <> expresses the modal nature of P.

Zach, if you're not going to listen to me, at least listen to James Anderson. Trust me, *he knows*.

5. Gentlemen,

I want to thank you for taking the time to refute Dr. Moore's assertions on my behalf. I wish I had more time to do so myself. However, given the fact that I work a full-time job, I'm the pastor of a new Reformed Baptist Church plant, I'm a daddy, a husband, and a seminarian, doesn't leave much time for "jogging the blogs." GeneMBridges can testify to this as he's a faithful attendee of our church and a frequent writer for the Triablogue.

May God richly bless you all as you serve the King through your apologetic endeavors!

Pastor Dustin S. Segers

6. Paul-

That's the first time I've seen you add modal notation to a modus ponens.

Again, how is this written in natural language? I'm struggling to understand the presuppositional argument, but everytime I see it, it's different. Is it a biconditional statement, or is it a modal modus ponens?

7. James-

"It should be obvious that For X to be the case, Y has to be the case (i.e. For Sam to be thinking about his lunch, Sam has to be thinking) is equivalent to If X is the case, then Y is the case (i.e. If Sam is thinking about his lunch, then Sam is thinking) rather than If Y is the case, then X is the case (i.e. If Sam is thinking, then Sam is thinking about his lunch)."

It's not that obvious to me in the presuppositional argument, but I'll take your word for it here. In that case, it's a simple modus ponens, and there's no foul. But surely you can anticipate that there's going to be the refutation from atheists that If X then Y is a non sequitur.

"Actually, to be still more precise, the claim For X to be the case, Y has to be the case is better translated as Necessarily, if X is the case, then Y is the case (which captures the modality indicated by the phrase "has to be")."

This isn't that obvious to me. Why is X the necessary clause? It seems to me that "has to be" indicates that Y is the necessary clause. I would write it: Necessarily, if Y is the case, then X is the case. Does this escape Affirming the Consequent if it's expressed with modality? Or is this equivalent to saying, "If and only if?"

8. Paul:

When did you become a Triablogger?

9. centuri0n,

Steve asked me sometime last week.

Zach,

Zach, when did you see it as a bioconditional? Based on when I said, *depending on what Dusin SAID* you could write P <--> Q. But the point was that the *has* would still be in the consequent position. You translated it wrong. Why can't you get this?

"Again, how is this written in natural language? "

You translated Dustin's argument wrong. Are you conceeding that? This is a different question you're asking. The point of my post was that you translated Dustin's argument wrong. Repetative learing, hopefully.

"I'm struggling to understand the presuppositional argument, but everytime I see it, it's different."

But this has nothing to do with how you translated Dustin's argument. Anyway, what "presuppositional argument." There are others besides TAG. Do you mean TAG?

And, it's not "different." Dustin's was the same. And, I've expressed it modally by saying "possible" I just didn't use <>. Indeed, virtually everyone (Christian and non), uses modus ponenes as the form of a TA. What is so hard to get? Basically, if intelligible experience is possible, then God...

Now, of course we could debate the support for the premise for years.

But, again, you translated Dustin's argument wrong.

"It's not that obvious to me in the presuppositional argument, but I'll take your word for it here. In that case, it's a simple modus ponens, and there's no foul."

I've been telling you that for years.

"But surely you can anticipate that there's going to be the refutation from atheists that If X then Y is a non sequitur."

And surely you can anticipate that we say it's not. ;-) How was *that* helpful, Zach?

"This isn't that obvious to me. Why is X the necessary clause?"

He didn't say that, did he? he said: necessarlily, if x then y. That's not the same as saying necessarily x.

10. Paul-

"Zach, when did you see it as a bioconditional?"

I didn't. You said it could be written as P<->Q. Is this the case or not? If so, then please point me to the resource that shows "for-has" becoming a biconditional, because I can't find one. If not, then why did you bring it up?

"You translated Dustin's argument wrong. Are you conceeding that?"

Not yet. First you said that it was a biconditional, but he didn't use "if and only if." So I don't think that holds. Now you're saying that it's a modal modus ponens. But I don't see that language in his argument. Maybe he should have written it more clearly- that's why I want to know how you would state it in natural language, to compare to what he wrote. If your argument is different from his, then I don't think I need to admit that I treated his argument unfairly.

"Anyway, what "presuppositional argument." There are others besides TAG. Do you mean TAG?"

Sure, unless you'd like to get back to the Transcendental Argument for the Existence of Beer. ;)

"What is so hard to get? Basically, if intelligible experience is possible, then God..."

Well, now, that's fine. I said in my original post that I'd be fine with a standard modus ponens. If X then Y. No big deal. Dustin didn't use if-then, he used for-has. I've yet to see a standard modus ponens argument that uses for-has. Or, alternatively, one that uses a parenthetical addition explaining that Y is the precondition for X.

"I've been telling you that for years."

I know, but you haven't been consistent with that. Do standard modus ponens have parenthetical additions?

"And surely you can anticipate that we say it's not. ;-) How was *that* helpful, Zach?"

Well, obviously. Now, admittedly this is tangential to the point of my original post, but if that's the case then the air is let out of the argument- it doesn't carry any weight outside of the Christian worldview. The attractive aspect of the TAG was that it could be used to force the atheist's hand, because he can't refute logic. But if it's just a simple modus ponens, then who's afraid of the big bad TAG? Not me.

11. well, you can lead a horse to water but you can't make him drink.

zach, not only have you mistranslated Dustin's argument, but yu're also misrepresenting me. Here's a challenge: quote my comment on bioconditional. I don't know why you're stuck on that??? I simply said that "DEPENDING oh what Dustin SAID, it could be translated as a bioconditional. I didn't read the post, so I don't know. Anyway, you ask why I brought it up? Well, as I said, because even if it was a bioconditional the Y would still go in the nconsequent position.

Also, your asking for me to back up the claim. I guess my word, the word of a Ph.D. in philosophy, the links I gave, is not enough. All you're doing here is getting people to laugh at you and atheism. Tell you what, go to your local college logic prof and ask him. Other than that, I can't force you to accept truth.

Also, show where I have not been consistent. All you're doing here is showing your ignorance. Guess what, standard modus ponens don't have *any* statements! Paranthetical or not. To even ask that shows your ignorance. Zach, where's a statement

P -> Q
P
/Q?

Zach, those are symbols. I can put what I want.

Moreover, yu claims about for-has not being "standard" is so sophmoric I don't know what to tell you. Guess what, it does not have to be! Sheesh! Have you even got to the chapter in your logic book where your translate ordinary language?

I mean, what you're saying is like if I wrote this:

p1. I went to the store.

and then you complain because I didn't write:

p1'. All Paul is a store-goer.

The more you type the more you show the level you opperate at.

Also, why keep trying to change the subject? The point is: you translated Dustin's argument wrong. Your stupid statement about TAG is just more evidence that you are unarmed in this battle of wits.

I think I've said all that I care to here, I won't be responding anymore.

12. Paul-

"I think I've said all that I care to here, I won't be responding anymore."

Fair enough, but I'm still not clear on the issue. You or anyone else can feel free to continue this with me by email.

I'll drop the bioconditional argument. I'm still curious why you would have brought it up at all if you didn't think it was correct, but whatever.

"Zach, those are symbols. I can put what I want."

Right, but each symbol represents a statement, right? Like "grass is green." Or, "humans are mammals." I've just never seen:

If P, then Q (because Q is the precondition for P)

as an example of a standard modus ponens anywhere.

"Have you even got to the chapter in your logic book where your translate ordinary language?"

Yeah, strangely enough there's no "for-has" example. You say that it's directly equivalent to if-then. I still disagree. I think it would be more appropriately written X only if Y. Just look at it:

For X to be the case, Y has to be the case.
X is the case only if Y is the case.

Aren't both propositions equivalent? I think so. But when you use "only if" that makes X the necessary condition, and so we're back to the fallacy.

The problem, I think, is not that I've translated Dustin's argument wrong. The problem is that there's no formal establishment of the presuppositional argument. Dawson's made this same point before, so I won't belabor it, but you might want to think about putting some effort into making a formal, orthodox undertstanding of the thing. Because until you do, there's going to be lots more people than just me who are going to take a crack at figuring out what exactly it is.

13. Zachary writes:

For X to be the case, Y has to be the case.
X is the case only if Y is the case.

Aren't both propositions equivalent?

Roughly, yes. At any rate, the direction of the conditionality is the same in both cases.

But when you use "only if" that makes X the necessary condition, and so we're back to the fallacy.

No. If X is the case only if Y is the case, then Y is a necessary condition of X. Think about it. (Cf. Sam is thinking about his lunch only if Sam is thinking.)

The problem, I think, is not that I've translated Dustin's argument wrong. The problem is that there's no formal establishment of the presuppositional argument.

Au contraire, the problem here is simply that you mistranslated Segers' argument.

14. James-

Thanks for picking this up.

You agree that "X only if Y" is an accurate rewording of Dustin's argument. But you argue that Y is still a necessary condition of X, and so I suppose that you would also argue that "X only if Y" is equivalent to "If X, Y?"

But if you notice section 3 of the Stanford Encyclopedia link that Paul posted, this argument is questioned. The author writes, Since not all uses of "if" in English state a uniform kind of condition, there is no general conclusion that can safely be drawn about symmetry, or lack of it, between necessary and sufficient conditions. Nor will it be right to claim that sentences like "if p, q" are generally paraphrasable as "p only if q". (emphasis mine)

Depending on the specific propositions, the necessary condition precedes "only if" in a proposition, as seen in example (iv). What are your thoughts on this?

The author also submits a method for determining sufficient and necessary relationships, as seen here:

B is a necessary condition of A =df the absence of B is a sufficient condition of the absence of A

Given the identity of the variables in the presuppositionalist argument, I would say that this relationship is reversed. That is, God is not a necessary condition for logic, but logic is a necessary condition for God. Is it merely possible that because of how Christians view the relationship God and logic, the argument is valid, but because of how atheists (or non-Christians) view the relationship, the argument is fallacious?