Wednesday, July 08, 2009

Response from James Anderson

I am pleased to report that Mr. Anderson has replied (here) to my previous post (here) regarding irresolvable paradoxes.

Mr. Anderson indicates that he does not accept the following:

(P1) The situation that both proposition P is true and P is false (at the same time and in the same way) is a possible situation for any given P.

This is, at least to my mind, some progress in our discussion. I view P1 as being representative of a general acceptance of paradoxes.

I do recall that Mr. Manata had characterized Mr. Anderson's position thus: "James Anderson sets out to show that certain doctrines of the Christian faith are paradoxical, but may be reasonably believed in spite of this feature (if not because of it). Anderson also argues that these doctrines are not actually contradictory, but merely apparent." (source - emphasis omitted)

I don't have a problem with merely apparent contradictions. I have a problem with actual contradictions. Given that Mr. Anderson does not appear to subscribe to what I have called the "general acceptance" view of paradoxes, I wonder whether Mr. Anderson would even subscribe to "special acceptance" view?

The special acceptance view would be (continuing the numbering from my previous article:

(P5) The situation that both proposition P is true and P is false (at the same time and in the same way) is a possible situation for a given proposition P iff further condition FC is met.

P5 is not liable to the same critique as P1 if (for P5) FC is met. However, I'm not aware of any good reasons to accept P5. However, again, I'm not sure that Mr. Anderson accepts P5. In fact, Mr. Manata characterized Mr. Anderson's position as: "If real contradictions could be true, then the desire to preserve orthodox interpretations is gone. Indeed, one could no longer object to heterodox statements." Assumed, of course, is that the desires to preserve orthodoxy is not gone. I should point out that I do fully agree with Mr. Anderson in this regard.

This makes me think that Mr. Anderson also would not accept P5. I hope he'll stop by and confirm that he does not accept P5.

In fact, I think part of the issue is that I am using "paradox" in a rather stronger form from Mr. Anderson. Mr. Manata claimed that Mr. Anderson defines paradox with the following:

"X is paradoxical [iff] X amounts to a set of claims which taken in conjunction appear to be logically inconsistent."

But, of course, I have no problem with apparent logical inconsistencies, so long as they are merely apparent contradictions (MACs). My problem is when apparent logical inconsistencies are also actual logical inconsistencies. Mr. Anderson's definition is broad enough to include actual and apparent inconsistencies (AACs), which is all that my narrower definition includes. My definition excludes merely apparent contradictions, while his includes them.

Now, I notice that Mr. Anderson's definition could be made to be completely separate in domain from mine if he were to add the word "only" before "appear." In other words, with that additional qualifier Mr. Anderson's definition would no longer include AACs, whereas mine would consist solely of AACs.

(There is a further category we could add to the discussion: non-apparent actual contradictions (NACs). This category isn't especially useful to our discussion, although it serves to remind us that there may be undiscovered contradictions.)

Furthermore, some of Mr. Manata's comments in his review of Mr. Anderson's work appear to reflect an understanding that the "only" that is missing from Mr. Anderson's definition should be implied. Mr. Manata writes:
Note well the qualifier ‘apparent.’ Thus, a paradox does not entail a logical inconsistency per se, just the appearance of logical inconsistency. This definition “presupposes that a meaningful distinction can be made between apparent and real contradiction.”
(internal quotation apparently from Mr. Anderson)

As a strictly logical matter, the definition quoted above does not presuppose that a meaningful distinction can be made between apparent and real contradictions. It evades that issue, since real contradictions often are also apparent (though sometimes they are secret).

Anyhow, rather than continue to speculate, I'd just pose the question to Mr. Anderson who (I hope) has not given up on reading my comments here.

Is P5 your position?

Did you mean to imply "only" in the definition of paradox that you provided?



Anonymous said...

Well now, wasn't that simple? Not!

I confess I was going along fine with Mr. Anderson's rebuttal or responses until I came to this, #5::::>

"....5. TurretinFan adds by way of conclusion: “I don’t see any good reason to accept the existence of irreconcilable paradoxes.” I don’t want to be uncharitable, but I suspect he says this because (i) he hasn’t read much if any of the literature on philosophical paradoxes and therefore doesn’t appreciate how challenging some of them are to resolve and (ii) he hasn’t read much if any of the literature on theological paradoxes, particularly on the difficulties of explicating the doctrines of the Trinity and the Incarnation in ways that are both orthodox and non-paradoxical. I could be wrong about this; if I am, it shouldn’t be any trouble for him to set me straight...."

May I jump out of my skin and exclaim: "Oh please, come on Mr. Anderson"!

Who gives a hoot whether or not TF has or has not read anything on philosophical or theological paradoxes?

The reality is simple. God is.

Can you answer me one question? Where is the paradox in "God is"?

While sitting around at the morning men's meeting of my Church, recently, one of the Minister's was trying to get around the parables of Jesus. I simply said, the only reasonable answer to any parable Jesus told is death. Every parable should remove the paradox and simply cause your eye to open and "see" your own pending death on earth all the while living on earth for the Glory of God. We preach Christ crucified, a death/life proclamation. Is that a paradox? No. Why? All parables point to "one" Truth. The Truth is "Self" Evident to those God has given Him to, as in what Jesus responded to Peter after Peter answered Jesus' inquistion of Himself, "You are the Christ, the Son of the Living God".

So Mr. Anderson's "slight" at #5 seems to me to try to redirect the plain meaning of Truth put over, directly, or indirectly.

God is. God is Eternal, having no beginning or ending. Are there contradictions to the Truth formed and evident as a theological paradox or a philosophical paradox? Certainly, in the temporal sense.

One has to ask then, how did #5 of Mr. Anderson's response move the ball further to the one's end, so that His beginning can begin to take shape and be enjoyed before leaving this present course, these created heavens and earth?

And I will add two final points. TF's response hereon is quite "charitable" all the while some may take mine as otherwise!

THEOparadox said...


I'll let James speak for himself, but here's what I've gotten from my reading of his book (so far), and my own studies. This may get a tad complicated, but I'll try to explain as clearly as I can.

In considering Anderson's definition of paradox, I've taken the "ONLY" for granted. I think if you read his book, you will see why. The "only" is implied everywhere in the development of his argument. On my reading, he never proposes that an actual contradiction is true, under any circumstances or conditions. He only claims that some true propositions appear to be contradictory when taken in conjunction with other true propositions. I've documented a clear example of this on my site, in dealing with the following Biblical statements:

B1) God alone is good (Luke 18:19, Mt. 19:17, Mark 10:18)
B2) Some people are good (Luke 23:50-52, Acts 11:22-24)

The same Greek word for "good" is used every time.

If we do not embrace Biblical paradox, the two statements force us into this conclusion: Either some people are God, or the Bible contradicts itself. This is not very appealing. The only alternative I find is Biblical paradox: the Bible APPEARS to contradict itself, but doesn't ACTUALLY contradict itself. I explored a possible solution for this, and concluded that although the two statements APPEAR to be contradictory, they are both true in different, non-contradictory senses (which are Biblically defined, based on further revelation). I enlisted Jonathan Edwards for support.

Although I resolved the paradox in that case, with a little less revelation we would have been left with what appears to be an unresolvable contradiction in the Bible. But let's never confuse that appearance of contradiction with actual contradiction. Resolution is only possible where there is enough further revelation to warrant a resolution. However, what are we to do in cases where the Bible doesn't give us enough information to form propositions that line up in simple, logical formulas that lead to a full explanation? It seems that sometimes we're left with the appearance of a contradiction, simply because we don't understand God's ways without His help, and He hasn't helped us enough to satisfy our rational demands.

As for P5, I can't claim any special expertise for addressing it, but it seems obviously false at a first reading. I can't think of a "further condition" (FC) that would make the law of non-contradiction invalid. Other than, say, a decree from God to invalidate logic. I don't see that happening.

If you are going to say the FC is that the statement is Biblical, I think this again misses the point. Paradoxes arise from "a set of claims" that (only) APPEAR to be contradictory," not a direct negation of one proposition by another (as in, "A is both true and false, at the same time and in the same way," - which is essentially P1 - and P5 fits in the same category). In the example above, this would equate to:

B1) God alone is good
B2) God is not good

If the Bible said that, we would have a serious problem on our hands.

I do hope James will comment here, since you're asking some good questions that ought to be addressed. Clarity is sometimes difficult to achieve, but always worth the effort.


Turretinfan said...

"In considering Anderson's definition of paradox, I've taken the "ONLY" for granted."

It may well be intended. I do hope he will confirm this.

James Anderson said...


Thanks for the follow-up.

Here's the relevant section from my book:

"As I will be using the term, [paradox] is synonymous with apparent contradiction. A 'paradox' thus amounts to a set of claims which taken in conjunction appear to be logically inconsistent. Note that according to this definition, paradoxicality does not entail logical inconsistency per se, but merely the appearance of logical consistency. Of course, what appears to be the case very often is the case -- but this definition is deliberately adopted so as not to beg any crucial questions about the logical status of Christian doctrines." (pp. 5-6)

Given this definition, an actual paradox must be one or other of the following:

(1) an apparent-and-real contradiction

(2) an apparent-but-not-real contradiction (what I call elsewhere a merely apparent contradiction)

I argue in the book that paradoxical Christian doctrines are instances of (2); more significantly, I argue that it is reasonable for Christians to believe those doctrines even while they cannot resolve the paradoxes (by "rational massage", as Clark memorably put it).

I hope this finally clarifies matters.

James Anderson said...

BTW, I'm still at a loss to know exactly which comments of mine caused your concerns in the first place. As far as I know, I have always been absolutely clear that I reject real contradictions.

Turretinfan said...

Hopefully I am fair in saying:

1) Your term "paradox" is broad enough to include MACs and AACs, but

2) The only paradoxes (using your definition) that you think we should accept are MACs not AACs.

If so, then (from where I'm standing) most of our disagreement has simply been semantic (i.e. over what the "right" definition of "paradox" should be).

At the risk or trying your patience, have I reasonably represented you now?