>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?

-TurretinFan