Turretin Fan did a little post on paradox in which, in one important respect, he comes down on the side of Gordon Clark rather than Cornelius Van Til:
http://turretinfan.blogspot.com/2009/04/paradoxes-and-christian-faith.html
Before I say anything else, permit me to say that TF is very different than Sean Gerety. TF knows how to argue for his positions, and does so on a regular basis. He’s a credit to his cause.
I’m going to zero in on one objection he raises:
“The idea that something is irreconcilably contradictory but not truly contradictory is an odd concept. It is so odd that it leads one to believe that, vis-à-vis the human mind, these are real contradictions that Van Til is talking about (although for God they are not contradictions). That's a bit troubling, since it seems to open the door to a denial of the law of non-contradiction at least as far as the human mind is concerned.”
“There is, however, a good reason to think that there are no such situations, at least because we have a very strong shared intuition that the law of non-contradiction is universal and applicable to the human mind.”
I find this objection puzzling. How would the law of non-contradiction preclude the possibility that truth may appear to be contradictory to the human observer?
We’re dealing here, not with things as they are in themselves, but a relation between the object of knowledge and the subject of knowledge.
Given the universality of the law, TF would have to take the position that not only are apparent contradictions impossible in our experience of Scripture, but they’re impossible in our experience of the world. Nothing true could ever confront the mind as apparently contradictory or paradoxical.
But surely it’s trivially true to come up with counterexamples. For instance:
“Abu Mazen was the first PLO official to visit Saudi Arabia after the Gulf War in January 1993.”
“Mahmoud Abbas was the first PLO official to visit Saudi Arabia after the Gulf War in January 1993.”
These two statements are formally contradictory. Does this mean that one or both statements are false?
As a matter of fact, both statements are true. The contradiction is apparent rather than real.
We need to distinguish between different named individuals and differently named individuals.
So, according to TF, does the law of non-contradiction preclude the possibility of apparently contradictory truths?
Or does it only preclude the possibility of insoluble apparently contradictory truths?
But even if he takes the weaker position, surely there are situations in which we lack sufficient information to resolve an apparent contradiction.
In the example I just gave, if the only information you had to go by were these two statements, you’d be unable to prove that both statements were true.
We just so happen to have additional information about this individual. We happen to know that he goes by more than one name.
I don’t see how the law of non-contradiction creates any presumption against the possibility of contradictory truths in human experience. The law of non-contradiction applies to the nature of truth, and not the perception of truth.
I’d add that I don’t think Van Tilians like James Anderson invoke paradox to explain examples of alleged numerical, nominal, chronological, or citational discrepancies in Scripture.
There's a lot of meat in this post. I'd to take a scavenger's approach and peck it a bit. Perhaps with more pecks to come:
ReplyDelete"I find this objection puzzling. How would the law of non-contradiction preclude the possibility that truth may appear to be contradictory to the human observer?"
My concern is not about every scenario where the truth may appear to be contradictory to the human observer. My concern is about the scenario where two statements appear to be contrary to every possible human observer even having all the information that humans can have that would help reconcile the statements.
So, that end, while the two comments:
“Abu Mazen was the first PLO official to visit Saudi Arabia after the Gulf War in January 1993.”
“Mahmoud Abbas was the first PLO official to visit Saudi Arabia after the Gulf War in January 1993.”
might seem to be contradictory on their face, they could be reconciled if those names are actually the name of the same person.
I'm not even bothered by apparent contradictions in the form "Answer a fool ... don't answer a fool," where the resolution is (essentially) that the phrases must be understood contextually.
I'm bothered by the idea that there are irresolvable contradictions in the form of:
A is true and
A is not true
Where A (and "is" and "true") is being used in a univocal sense.
-TurretinFan
Paul M. ... yes, one of my concerns is that my differences with Van Til and company are most semantic.
ReplyDeleteIs it wrong to say that Van Til's position is that there are "paradoxes" whose solutions are essentially incommunicable to mankind?
TF,
ReplyDelete"I'm bothered by the idea that there are irresolvable contradictions in the form of:
A is true and
A is not true".
Well that's helpful for us to reach resolution. This (above) is not the kind of contradiction Anderson has in mind.
Your example is an example of an explicit apparent contradiction (all contradictions are apparent contradictions, but paradoxes are merely apparent).
The kind Anderson has in mind are implicit contradictions, where upon reflection of other necessary truths yield a formal (not explicit) contradiction.
So, Anderson specifically says that the paradox of the trinity is not expressed as something like:
"There is only one God
and,
there is not only one God"
For further elucidation see Anderson, pp. 108-111).
So, given what bothers you, you shouldn't be bothered by a Van Tillian analysis of theological paradox. :-)
What would be interesting is to see you how you guys tackle Eunomius of Cyzicus on this question, since it is on the basis of the principle of non-contradiction and the opposition between Ingenerate - Generate that the Son cannot be God.
ReplyDeletePhotios
It should be noted that the comments apear out of order since I deleted my comments to add something else, that's why TF is replying to something that appears below him.
ReplyDeleteTF, you ask:
"Paul M. ... yes, one of my concerns is that my differences with Van Til and company are most semantic.
Is it wrong to say that Van Til's position is that there are "paradoxes" whose solutions are essentially incommunicable to mankind?".
In one sense, I would like talk to move forward to Anderson's improvment on talk of paradox. I'd view it as the tools of philosophical analysis applied to Van Til's claims.
So, with that caveat:
There is no claim to any paradox being necessarily insoluble, though that could be a possibility.
Again, I'd point to perhaps a more bite-sized case---that of the spacelanders and flatlanders.
Now, it may be that the revelation of a 3-D cone as "it is a square and it is a circle" to the 2-D flatlanders will always remain isoluble due to their very nature as 2-Dedness.
Or, for example, say that the spacelanders gave them the mathmatical formula for volume. They revealed the solution as: 1/3 * 3.14 * r2 * h = v.
What god does this do flatlanders?
So, though I leave it as a live possibility that a solution may be given, cognitive rest acheived, tensions removed (all part of leaving the world of tension as we live in the already/not yet world of tensions), I grant that the solution may be something like the solution to the volume of a cone is to the flatlanders. What good would it do them? Their very nature seems to preclude understanding the solution, seeing how a 3-D object makes sense.
However, given the nature of spacelander as good and trustworthy, say, spancelanders knowledge of the object being revealed--so knowledge transvers (via transivity principle of testimonial knowledge), the individual warrantedness of the propositions, (fill in other epistemic desiderata) etc., the flatlanders would still be rational in accepting, in a limited and mysterious way, that "the object is circular and triangular."
(Of course, the equivocation is on "vertical" and "horizontal". But even that information, while showing that there's no explicit contradiction, still seems mysterious and can result in an implicit merely apparent contradiction.)
And of course, Anderson is free to disagree with my defense of his position, if there are errors in my post it shouldn't be taken to necessarily represent Anderson's argument. I'm mostly going off memory.
ReplyDeleteabove I said a 3-D cone was revealed as "it is square and it is circular," that should read, rather, "it is *triangular* and it is circular"
ReplyDeleteSteve,
ReplyDeleteVery good post!
Paul,
Very good defensive maneuver.
Turretin Fan,
Very good objection to paradox, and I think it has been answered well. I'd like to see more discussion of this type between respectful and thoughtful people like yourself and Paul.
Also, I would invite you to take a stab or two at my recent post, The Logic of THEOparadox:
http://theoparadox.blogspot.com/2009/04/10-affirmations-of-theoparadox.html
There are 10 brief statements there which I think make a case for embracing paradox on logical grounds.
I'm reviewing Anderson's book chapter by chapter, and since I'm only on chapter 3, I don't know if my approach is lining up with his on the deeper philosophical level. Of course, he's three times as smart as I am, so I'm probably not even scratching the surface of his work.
All,
Here's another example of a formal, not explicit, paradox:
Paul M mentioned the already/not yet. In the New Testament, we are said to be redeemed (past tense), but we are yet to be redeemed (future tense). We are said to be saved (past), being saved (present), and yet to be saved (future). We are said to be sanctified (past), being sanctified (present), and yet to be sanctified (future). These are not explicit contradictions, but they set up formal contradictions of chronological procession which, thankfully, can be resolved. God has given us the needed information and as a result we have extensive theological materials explaining it in detail. We have been saved (in one sense), we are being saved (in another sense), and we are yet to be saved (in yet another sense).
But what are we to do with the hypostatic union? That one's not so easy, because God doesn't reveal the "senses." And I'd venture to say that some of the information needed to resolve it is missing. In fact, based on the flatlander/spacelander analogy, couldn't we say we don't have the TYPES OF THOUGHT or the CATEGORIES OF THOUGHT needed to resolve it? Call me crazy ...
I should be careful, someone may take me up on that.
Grace & peace,
Derek Ashton
Paul M.: You may recall the "upward but not northward" (or something to that effect) line from the book. It conveyed the difficulty that the 3-D being had in communicating 3-Dness to a 2-D being.
ReplyDeleteThere are a couple of branches that I would stem from that.
1) There is no obvious reason that God could not communicate truth to us without irreconcilable contradiction. (but perhaps this is not the claim from the VT side?)
2) There is no obvious reason that God would not communicate truth to us without irreconcilable contradiction, without telling us that the two things are reconcilable (just not with the information we have or can have). (but perhaps this also is not the claim from the VT side?)
3) Although it is difficult to imagine a 4th spatial dimension, we three dimensional creatures are able to imagine the concept, and even to create Klein jars to help represent the concept. So, while Flatland is an interesting book, it seems to defeat itself.
4) In fact, unfortunately, virtually any attempted example is going to fall into one of two piles:
a) Real contradictions posing as merely apparent contradictions; and
b) Apparent but resolvable contradictions.
5) So, perhaps, my question is why one would think that there were merely apparent (not real) but unresolvable contradictions?
-TurretinFan
TF,
ReplyDeleteAd 1: To use the term "contradiction" is a question begging epithet. It is furthermore question begging since there are arguments that God's revelation of himself has some paradoxicality to it. And, while there may not be "an obvious reason," there are reasons.
Ad 2: I don't know if they are ultimately reconcilable or not. My point was I make no claim either way. As far as what God would or wouldn't do here, I see no reason to place such constraints on him. Indeed, this could be question begging too. Say that any "solution" would be incomprehensible to us, just because of the nature of the solution. In that case, why would he tell as that there is a solution but that it wouldn't make sense to us? This move would seem to move in the direction that the Bible is like a science, philosophy, or political textbook, when it's main purpose is to tell us how to get right with God.
Indeed, there are many things we know that we may never know the reason but are required to trust God. Will God provide the ethical calculus showing how ordaining 1,000 child molestations this year rather than 999 was actually for the greater good, or how it gave him more glory?
So, if it is irreconcilable for us, I don't see why he would need to be so pedantic as to tell us that (indeed, he never gave Job a reason, and Job's friends could have said, "There's no obvious reason why when you get your sit-down with God, he won't tell you the reason. Fact is, Job couldn't fathom it. He spoke to soon.) If it is reconcilable for us when we get to heaven, or even later here on earth, I don't see why one would think God would tell us that.
Ad 3: Analogies always break down; however, I'm unsure a 2-D being would understand "solutions" to volume.
"Similarly, we can discover what some four-dimensional objects look like by viewing aspects of them in three dimensions. But like the square, we are limited in understanding the whole nature of these objects."
http://www.geom.uiuc.edu/docs/forum/polytope/
Furthermore, we might also live in 4-D space. So your counter would fall here.
But however this is cashed out, the differences between us and God, our kind of being and his, is so vast as to not have an appropriate creaturely analogy.
Ad 4: There's a fatal missing element for your argument to work: resolvable to who? Why think it must be man?
Ad 5: To not be dogmatic and leave open that possibility. I have no reason to suppose that man must be able to resolve every single apparent contradiction. Why think a thing like that?
That seems like a pretty stong claim, I'd like to see how an argument for that would go.
TF,
ReplyDeleteI'm not a big fan of theological paradox, but I disagree with (i). There is no obvious reason that God could not communicate truth to us without paradox–provided that reality is sufficiently simple that the human mind can grasp it as is.
Speaking for myself, I find that assumption rather implausible. We run into paradoxes in logic, math, and science. That's because the human mind is trying to penetrate a reality which is more complex than the mind which tries to penetrate that reality.
Hi TF,
ReplyDeleteI think your answer to the question i asked you on your blog bears on your comments here:
I asked: "If you felt a view was unorthodox would you gladly affirm it? Even if it were rational?"
You replied: "If a doctrine is Scriptural, I will accept it, even if it gives me goosebumps. I'm not too worried about the label "orthodox" except to the extent that it is synonymous with "Scriptural".
Paul M. wrote: "Ad 1: To use the term "contradiction" is a question begging epithet. It is furthermore question begging since there are arguments that God's revelation of himself has some paradoxicality to it. And, while there may not be "an obvious reason," there are reasons."
ReplyDeleteI certainly didn't intend it as an epithet. I thought you yourself used the term "contradiction" in the definition of paradox: merely apparent contradiction. If anything is question-begging or epithetical in my comment, one might argue it is the "irreconcilable" part, though again I was basing that on what I understood your claim regarding paradox to be.
As I hinted at, in my response to Steve, I think the issue of whether "no obvious reason to think 'x'" is an appropriate standard is partly one of what our default position ought to be.
Paul M. wrote: "Ad 2: I don't know if they are ultimately reconcilable or not. My point was I make no claim either way. As far as what God would or wouldn't do here, I see no reason to place such constraints on him. Indeed, this could be question begging too. Say that any "solution" would be incomprehensible to us, just because of the nature of the solution. In that case, why would he tell as that there is a solution but that it wouldn't make sense to us? This move would seem to move in the direction that the Bible is like a science, philosophy, or political textbook, when it's main purpose is to tell us how to get right with God."
I think the intuitive argument here (and I don't mean to suggest that it has been developed in a rigidly and strictly logical way, or that you need to accept my gut on this) is that if God is going to tell us things that appear irreconcilably contradictory, he would also (as an apology for his truth) reveal to us that there is a reason why we cannot resolve these apparent contradictions.
Paul M.: "Indeed, there are many things we know that we may never know the reason but are required to trust God. Will God provide the ethical calculus showing how ordaining 1,000 child molestations this year rather than 999 was actually for the greater good, or how it gave him more glory?"
I'm not suggesting that God needs to show his sums or justify his actions. Nevertheless, I note that God has revealed specifically that he does not need to show his sums and justify his actions, which reinforces my intuition expressed in (2).
For me, at least, the problem of evil is an example of an apparent contradiction that many people wrestle with, but which is not only resolvable by God, but also answered in revelation (esp. Romans 9).
Paul M.: "So, if it is irreconcilable for us, I don't see why he would need to be so pedantic as to tell us that (indeed, he never gave Job a reason, and Job's friends could have said, "There's no obvious reason why when you get your sit-down with God, he won't tell you the reason. Fact is, Job couldn't fathom it. He spoke to soon.) If it is reconcilable for us when we get to heaven, or even later here on earth, I don't see why one would think God would tell us that."
Well ... someone wrote the book of Job, and whoever did got the reason. And Job provides a partial answer (even before Romans 9) to some of the more troubling issues relating to the problem of evil, with which so many people struggle.
But, of course, at some point, Job had not been written and Job was actually siting there with a potsherd. Although I pity (and praise for his patience) Job in that situation, I don't have a fundamental problem with the idea that it could be the case that there was no way Job could have figured out the solution to this dilemma without the revelation that came afterward.
What I would have a problem with, is if no amount of revelation could ever have resolved the issue.
Paul M.: "Ad 3: Analogies always break down; however, I'm unsure a 2-D being would understand "solutions" to volume."
Well, are you able to understand that the meta-volume of a 4th dimensional meta-cube is height*length*width*meta-length, where each is measured in meters? If so, why shouldn't the 2D being be able to understand 3D volume?
Paul M.: "Similarly, we can discover what some four-dimensional objects look like by viewing aspects of them in three dimensions. But like the square, we are limited in understanding the whole nature of these objects.""
ok
Paul M.: "Furthermore, we might also live in 4-D space. So your counter would fall here."
At least in some sense, the square lived in 3-D space.
Paul M.: "But however this is cashed out, the differences between us and God, our kind of being and his, is so vast as to not have an appropriate creaturely analogy."
What is interesting is that God is so often able to give us creaturely analogies to give us information about himself. I don't deny that the differences are infinite, but God is still able to communicate whatever he wants about himself.
Paul M. wrote: "Ad 4: There's a fatal missing element for your argument to work: resolvable to who? Why think it must be man?"
I'm framing the question in terms of human knowledge. As I mentioned elsewhere, if the Law of Non-Contradiction only applies to God, so be it - but then (as far as I know) there is no reason to deny that it also applies to men.
Paul M.: "Ad 5: To not be dogmatic and leave open that possibility. I have no reason to suppose that man must be able to resolve every single apparent contradiction. Why think a thing like that?"
The reason to address this goes (as noted above) to the nature of human knowledge, and specifically to the central issue of the law of non-contradiction.
Paul M.: "That seems like a pretty stong claim, I'd like to see how an argument for that would go."
The point is not that mankind has or will resolve every apparent contradiction, but that there is no constitutional barrier such that, even with revelation, such resolution is impossible.
-TurretinFan
TF,
ReplyDeleteAd 1: I did use the term contradiction with the antecedent qualifications, you didn't include them and so it could be taken that you were saying we affirm actual contradiction. I suggest we use AC for all apparent contradictions (which cover actual contradictions and paradoxes). I suggest AAC for all apparent and actual contradictions. And MAC for merely apparent contradiction.
As for as "irreconcilable." My position is that I am open to a MAC being reconcilable and it not being.
AD 2: I'm not sure how you're cashing out the claim "God would reveal to us the reason that they are irreconcilable." And, since I'm open to resolution, I'm unsure how this argument is supposed to work. Anyway, say that some are irreconcilable, I believe God has given is the information why this may be. Anderson cashes this out in greater detail in his book. I find similarities here with certain responses to the problem of evil; namely, some of the moves that have been made WRT the "Noseeum" response to the PoE.
Now, you say:
"I'm not suggesting that God needs to show his sums or justify his actions. Nevertheless, I note that God has revealed specifically that he does not need to show his sums and justify his actions, which reinforces my intuition expressed in (2).
For me, at least, the problem of evil is an example of an apparent contradiction that many people wrestle with, but which is not only resolvable by God, but also answered in revelation (esp. Romans 9)".
Of course, "For his glory", even allowing that it is the theodicy a lot of Reformed claim for it, doesn't help me understand why there were 1,000 molestations this year rather than 999. Would you be willing to grant that God's specific answer why he ordained 1 more might not be attainable to us, such knowledge being "too lofty?"
So, I trust God, I know he has a good reason for the evil he allows, however; I also am quite satisfied that I will never or could never know that reason. It may forever not "make sense" to me. I certainly can't "see" (now) how ordaining 1 more child molestation brings God more glory, has a good reason for it, etc., and...I might never be able to "see" how this works. That certainly seems possible.
Now, I don't think I have any MAC going on here with the PoE, that stretches my analogy to far. The use of my analogy is that I think it shows that it is posisble that there are some things we might not be able to understand even if God were to reveal it. If you grant that premise, then there's no reason to deny that the paradoxes which do exist (granting Anderson's argument) have a resolution understandable to us.
But besides that, I know some general reasons why irreconcilability might be the end game, and those are on the same level as the general greater good theodicy. So, to answer your question, I think God has revealed why a paradox might be irreconcilable for us. Yet, I do not claim that any actually are, some just may be. If so, I know why, and think no Christian should have a problem with the reason, even if they deny any actual paradox (which is another debate, because of Anderson is correct, and those doctrines are paradoxical, then you need to answer your own questions).
You then say:
"What I would have a problem with, is if no amount of revelation could ever have resolved the issue".
I guess at that point I just have to voice that I strongly disagree. I can't understand why you would think this. A 3 year old may understand some things, but eventually he gets to the point where no further revelation helps him as a three year old. Indeed, he probably wouldn't even understand the resolution to, say, some logical or mathematical paradox. Surely the gap between even a glorified human and God is further than a three year old human and Einstein. (Anderson covers a lot of the reasons for why in his book.)
I quoted a website thus:
"Similarly, we can discover what some four-dimensional objects look like by viewing aspects of them in three dimensions. But like the square, we are limited in understanding the whole nature of these objects."
You replied:
"ok".
I think that admission is more in my favor than you may think.
Paul M.: "Furthermore, we might also live in 4-D space. So your counter would fall here."
"TF: At least in some sense, the square lived in 3-D space".
Still seems to me that they can't "wrap" their "heads" around volumeness. They got the solution, so what's the problem?
And, in what sense are we divine? And is this sense enough to fully understand God? If not, and a paradox results from God's nature, and his incomprehensibility, why think we could grasp a resolution, especially when flatlanders can't fully grasp volume, and three year olds myriad logical and mathematical resolutions to paradox?
TF: "What is interesting is that God is so often able to give us creaturely analogies to give us information about himself. I don't deny that the differences are infinite, but God is still able to communicate whatever he wants about himself".
Of course, defenders of paradox don't deny that we have some truth about God. I also agree that God is able to communicate "whatever he wants" (depending on how it's cashed out). Again, as James mentioned at your blog, the question whether there are paradoxes should be answered first. But, again, assuming that their are, I wonder how to take you? He revealed what he wanted, and it came off paradoxical. And, let's say he was able to communicate the "solution" to us in human language, why think you could understand it? I could "communicate" in English Pythagoras’ theorem to a 2 yr. old, what good would it do him? Could he understand it?
TF: "I'm framing the question in terms of human knowledge. As I mentioned elsewhere, if the Law of Non-Contradiction only applies to God, so be it - but then (as far as I know) there is no reason to deny that it also applies to men".
I just don't follow this. God is not an AAC, we know this, how does it follow that he hasn't revealed himself as a MAC? I hold the LNC, why does that mean MACs will never arise? There seems to be some leaps you're making.
TF: "The point is not that mankind has or will resolve every apparent contradiction, but that there is no constitutional barrier such that, even with revelation, such resolution is impossible".
Again, maybe they will all be resolved at some time. However, if you're going to argue that irresolvability (by man) is impossible, then that's to make a very strong claim. I don't see how you could actually argue for something so strong. For me, I'm allowing that both are possible. I have a much easier burden. I think I have shown the possibility of irresolvaibility, even if you don't agree that it represents the actual state of affairs, in this case that has no bearing on the possible.
The "irreconciliable" aspect is the part that gives me acid indigestion. If you're not insistent on that point, perhaps there's no core dispute between us.
ReplyDelete-TurretinFan
TF,
ReplyDeleteAbove I thought you said you could live with some acid refulx.
I am not insistent, I'm just saying that it is possible that some could be irreconcilable. As far as I can tell, the indigestion comes from an afront to rationality, and I think Anderson has shown that this need not be the case.
If I may jump in here... to defend my insistence (not shared by Paul M.) on insolubility due to human limitations, and to answer TF's question about there being a "constitutional barrier"...
ReplyDeleteConstitutional barrier #1
Ontology. God is a different category of being than man is. He is holy. Why wouldn't we apply "otherness" to His thoughts as well as His moral character, intentions, etc? He does so Himself in Isaiah 55. I don't buy the exegetical twisting that tries to deny this.
Constitutional barrier #2
Intelligence. A genius may have an IQ of 200. If God's IQ could be measured accurately, it would be ... infinite. So who are we to think we can fully grasp His thoughts without any remaining apparent contradiction in our minds?
Constitutional barrier #3
Perception (or scope of knowledge). We can imagine a 4th or 5th dimension with a bit of mental strain. But there is no reason to suppose that we do not actually live in a 6-dimensional, or 40-dimensional, or 1000-dimensional universe. Why would an infinite God limit Himself to the few dimensions His creatures perceive? He created vast galaxies we will never know about, so why not a few extra dimensions, too?
Multiply the perceptual differences between Flatlander and Spacelander by 1000, perhaps more. Now, make Spacelander the most brilliant and logical communicator ever to exist. Make Flatlander a proud, self-reliant sinner who continually tries to make himself equal to Spacelander. You end up with perfect communication that in some cases cannot be adequately perceived. Now give Spacelander endless wisdom, and watch him use his communication skills in conjunction with Flatlander's misperceptions to prove that he is altogether other than Flatlander. That he exists on a different plane. Obviously, this is speculation. But it is deduced from a belief in God's omniscience, infinity and transcendence. It is also a furtherance of the analogy under discussion.
I got my wish . . . this is a really cool discussion. Now, is there any logical problem with my constitutional barriers?
Another shiny object caught my eye: "If not, and a paradox results from God's nature, and his incomprehensibility, why think we could grasp a resolution, especially when flatlanders can't fully grasp volume, and three year olds myriad logical and mathematical resolutions to paradox?"
ReplyDeleteIt occurred to me that actually three year olds are blissfully unaware of the logical problems, rather than by stymied and frustrated. It is only when we gain the wisdom of age that we start to think about how the magician probably used twins or a contortionist rather than just getting baffled and googly-eyed over the pretty lady being cheerfully sawn asunder.
Thus, to an extent, the affirmation of a strong view of the law of non-contradiction is a part of the maturity that comes with age and is one way in which we put away childish things.
-TurretinFan
Call me immature, but I'm firmly convinced that God's indescribable greatness is going to leave me "googly eyed" for all of eternity. I hope I never grow up, I'm a Paradoxes-R-Us kid!
ReplyDeleteDerek,
ReplyDeleteYou wrote: "God is a different category of being than man is. He is holy. Why wouldn't we apply "otherness" to His thoughts as well as His moral character, intentions, etc? He does so Himself in Isaiah 55. I don't buy the exegetical twisting that tries to deny this."
Leaving aside the Isaiah 55 issue (and allegations of exegetical twisting), God's otherness must be tempered by the fact that God does provide analogy from the creation as a way for us to understand him.
Any analogy breaks down if stretched beyond its limits, but within its limits, each such analogy accurately and truthfully represents God.
Since this is the case, we can have at least some true knowledge of God.
As for intelligence, that's really more of a quantitative measure than a qualitative measure. I certainly agree that quantitatively we are incapable of comparing with the thoughts of God.
Certainly, there are some things that are very hard to imagine. Nevertheless, at least mathematically, n-dimensionality is not that hard to grasp, once someone shows you how to understand it. (Of course, it is hard to visualize, but that's simply because we have visual senses that perceive 3 dimensions through stereoscopic 2 dimensional images).
The primary argument for Van Til's "qualitative" differences is the ontological argument, to be sure. It's an interesting question to ponder, but it's connection (if any) with human knowledge seems to be self-defeating. The less like human knowledge is divine knowledge, the less important divine resolutions to human conundrums becomes.
-TurretinFan
TurretinFan,
ReplyDeleteYou wrote: "God's otherness must be tempered by the fact that God does provide analogy from the creation as a way for us to understand him. Any analogy breaks down if stretched beyond its limits, but within its limits, each such analogy accurately and truthfully represents God. Since this is the case, we can have at least some true knowledge of God."
Agreed on all points. I'm don't subscribe to the Van Tillian idea of there being paradox in ALL our knowledge. Gordon Clark was right to poo poo that. We must acknowldedge that much of the Bible is crystal clear, yet there are aspects which are humanly impossible to understand.
TF: "As for intelligence, that's really more of a quantitative measure than a qualitative measure."
Does it have to be? If God's thoughts are "higher" than ours, as high as the heavens are above the earth (which in Hebrew thought is approximately infinite), why wouldn't they be of an entirely different quality? Are heaven and earth qualitatively different in the Hebrew mind? Are "finite" and "infinite" qualitatively different, or quantitatively? Perhaps both?
TF: "The primary argument for Van Til's "qualitative" differences is the ontological argument, to be sure. It's an interesting question to ponder, but it's connection (if any) with human knowledge seems to be self-defeating. The less like human knowledge is divine knowledge, the less important divine resolutions to human conundrums becomes."
This is why I propose a direct connection between some human knowledge and divine knowledge, but with the caveat that God's thoughts are qualitatively supra-human. His thoughts can be qualitatively different than ours without being completely imperceptible to us.
For example: God thinks a thought that is qualitatively different than man's thoughts. He communicates the thought to man. Part of the thought is perceptible by man, and part of it is beyond his capabilities. Man can rightly understand the thought to a point, but not comprehensively. Sometimes the humanly perceptible part of several of God's revealed thoughts seem to contradict, but it is only because man lacks the portions of those thoughts that are perceptible only to God.
So, from a qualitative standpoint, we can correctly perceive part of each thought He expresses. Picture an electrical circuit that is barely making contact. There's enough of a connection to conduct electricity, but there are numerous points at which the two sides are not connecting at all. You still have a complete enough circuit to accomplish the intended purpose. Similarly, God provides us with just enough unambiguous knowledge to draw the elect and just enough paradox to harden the unbelieving. This is loosely following Pascal's argument.
All of man's right knowledge is given by God and is therefore accurate (as far as it goes), but it is still incomplete. Our knowledge can never be comprehensive enough in quality or quantity to resolve certain paradoxes which would require a mind like God's to understand. So we are truly "thinking God's thoughts after Him," just not enough of them to provide complete coherence. Why? Because we are limited by human nature (a qualitative difference) and incomplete revelation (a quantitative difference). Add total depravity to the equation, and our inherent limitations increase all the more.
Blessings,
Derek
TF,
ReplyDeleteRegarding that "shiny objection"...
Kids don't get things all the time. They might ask, "How is there only one God, but Jesus is God, the Father is God, and the Spirit is God." If you've dealt with enough kids you'll know that tell them, "Well, he's one what and three whos," or "He is one in essence, three in person," fail to make it intelligible to them. But, take adults even. There are plenty of things that normally intelligent adults could not "understand," such as, maybe, the calculus of physics or suchlike. It seems to me an obvious truism that the "answer" may be too complicated for even a glorified mind to "get." If you want to disagree with this, then I ask again for the argument since it seems to affirm a very strong conclusion that I have no idea how it could be cogently argued.
"Kids don't get things all the time." True. My point was not that they got things: quite the opposite.
ReplyDeleteIf a three year-old is confused by the One God, Three Persons, issue, that's a precocious child.
-TurretinFan
TF,
ReplyDeleteI must admit that I've lost track of your objection.
I gave possible states of affirs where what appears paradoxical can remain irresolvable even if an "answer" is given -- due to the complexity of the answer and the limits of the human mind. To defeat this you need to argue that it is *im*possible. I have not seen that argument yet.
"I must admit that I've lost track of your objection."
ReplyDeleteDue to the complexities thereof and the limits of your mind, perhaps?
(just a joke)
You wrote: "To defeat this you need to argue that it is *im*possible."
Well, I do imagine that I could defeat it several other ways than that, but I didn't come here to defeat you (I'm neither that naive nor that proud). I mostly hoped to clarify a few things.
There are still a few scraps I'd like to peck at on the bones of the original post.
Steve asked: "So, according to TF, does the law of non-contradiction preclude the possibility of apparently contradictory truths?"
Answer: no.
Steve noted: "I’d add that I don’t think Van Tilians like James Anderson invoke paradox to explain examples of alleged numerical, nominal, chronological, or citational discrepancies in Scripture."
I would hope not. I assume not. Yet, of course, that is the very real risk of the position (at least in a misunderstood form), which is not (of course) an objection to the position. (i.e. I'm not arguing, 'Shut up, you might confuse people.')
TF,
ReplyDeleteI am using 'defeat' in its technical philosophical sense, as in, 'defeater.'
At any rate, I can only note that I've seen no reason to suppose that it is impossible that there might be a paradox unable to be solved at the bar of human reason. Perhaps you have one, as you suggest, but I don't know what it could be. Anyway, above you said you might not have that big of a problem since I make no claim that any paradox *must* be irreconcilable, so perhaps we can just split the diference.
I think, Paul, my main argument has had the form:
ReplyDeletea) There's only a particular form of "paradox" to which I object;
b) I haven't seen any good reason to make me think that particular form exists;
c) I think the burden of persuasion is on the person alleging that such paradoxes do (or could - I think you've perhaps only taken that lesser position) in fact exist;
d) Accordingly, I remain unpersuaded to adopt this concept of "paradox" even if I haven't positively demonstrated that they cannot exist; but
e) I do think that there is a strong (though perhaps not bullet-proof, I'm still turning it over in my mind) argument against their existence in the following form:
i) Suppose that there can be a paradox unable to be solved at the bar of human reason;
ii) Given (i), it would be either or a paradox or a real contradiction to say that there cannot be a paradox unable to be solved at the bar of human reason.
iii) We humans cannot tell the difference between paradox and real contradiction, because if we could the paradox wouldn't be an apparent contradiction.
iv) Therefore, if we accept that it could be that there is a paradox unable to be solved at the bar of human reason, we also should, in principle, accept that it could be that there is not a paradox unable to be solved at the bar of human reason.
Strictly speaking this is not a defeater, but it shows that the position that it is not possible that there could be a paradox unable to be solved at the bar of human reason is at least as strong as the position that it is possible that there could be a paradox unable to be solved at the bar of human reason.
-TurretinFan
Turretin Fan,
ReplyDeleteThis is not an admission of defeat, but a genuine compliment: that is the best argument I've ever heard against my own position.
Blessings,
Derek Ashton
TURRETINFAN SAID:
ReplyDelete“ii) Given (i), it would be either or a paradox or a real contradiction to say that there cannot be a paradox unable to be solved at the bar of human reason.”
You seem to be saying that any argument for paradox would, itself, be a paradoxical argument. Is that what (ii) amounts to?
If so, I don’t begin to see how that follows. To go back to my example of Abu Mazen and Mahmoud Abbas, if I argue that these two statements are apparently (indeed, formally) contradictory, is my argument itself contradictory? Is it self-contradictory to argue that two proposition are apparently contradictory? Surely there are ever so many examples to the contrary.
TF,
ReplyDeleteAd a: Clark, Robbins, and Gerety wouldn't like that, but that's fine. So, call the paradoxes you reject: paradoxes ultimately irreconcilable by man's mind: PUIMM
Ad b: I see no reason to claim that any PUIMMs in fact exist, they just might. If you disagree with this then you need a very strong argument. See below.
Ad c: Well, which is it? Have you seen no good reason why PUIMMs do exist or that they could or might exist? If the former, I haven't offered any such reasons. If the later, I gave you plenty. To defeat my general argument for the latter you would then need to make the strong argument that PUIMMs are impossible.
Your claim seems to imply that the human mind can in principle grasp any metaphysical distinction, no matter how refined or complex. For if there is at least one metaphysical distinction that could not be grasped by the human mind, it follows that there is at least one possible (i.e., consistent) state-of-affairs that would be paradoxical to us were God to describe it to us.
Ad d: That's fine, but your position goes far beyond what you can argue for it.
Ad e: You write:
"e) I do think that there is a strong (though perhaps not bullet-proof, I'm still turning it over in my mind) argument against their existence in the following form:".
Okay, shoot:
"i) Suppose that there can be a paradox unable to be solved at the bar of human reason;".
Okay.
"ii) Given (i), it would be either or a paradox or a real contradiction to say that there cannot be a paradox unable to be solved at the bar of human reason".
Given (i), it would only be a paradox. Remember, you are supposing that there is a paradox that cannot be solved or reconciled before the bar of human reason.
"iii) We humans cannot tell the difference between paradox and real contradiction, because if we could the paradox wouldn't be an apparent contradiction".
Au contraire, mon frère. First, that we can discuss things like MACRUEs and AACs, real and apparent, etc., shows that we can tell differences. Genuine distinctions can be made. We also know that there can be no actual contradictions in God's nature. If God exists, then God cannot be contradictory, so God isn't actually contradictory. We also know that relevant distinctions could be articulated, and Anderson lists several possible candidates. Anderson points to numerous possible unarticulated equivocations. Furthermore, each particular proposition in the paradoxical doctrine is warranted. Anyway, Anderson discusses this point in detail in his book. The bottom line is that we can make distinctions between MACRUEs and AACs, we do it all the time.
So, we can tell the difference. Second, however, that doesn't imply that we wouldn't have a paradox anymore. For if we are warranted in believing something is a MACRUE, then we are warranted in believing it is not an actual contradiction, while also maintaining the appearance of contradiction (via the implicit spelling out above, not explicit). If I have a genuine dollar bill and a counterfeit one, the ability t tell the difference doesn’t mean the counterfeit wouldn’t be a counterfeit anymore. The appearance of contradiction can be held while also denying the actuality of the contradiction.
"iv) Therefore, if we accept that it could be that there is a paradox unable to be solved at the bar of human reason, we also should, in principle, accept that it could be that there is not a paradox unable to be solved at the bar of human reason".
Yeah, this is just a non-sequitur.
"Strictly speaking this is not a defeater, but it shows that the position that it is not possible that there could be a paradox unable to be solved at the bar of human reason is at least as strong as the position that it is possible that there could be a paradox unable to be solved at the bar of human reason."TF, if it is not a defeater for the claim that "it is possible that there be a paradox irresolvable at the bar of human reason" then it is possible that there be a paradox irresolvable at the bar of human reason. You seem to be missing out on how strong of an argument you need to offer to deny the claim just expressed.
Again, to properly deny my claim you have to show that it is impossible that there ever be a paradox of such a complicated metaphysical nature that the distinctions needed to unravel the unarticulated equivocation couldn't be more complicated than a finite mind could handle.
That is what you need to argue against, and frankly, I am at a loss as to how you could argue it, or why you would argue something like that.
Sincerely Perplexed,
PM
I should say, with Steve, I didn't really understand what you meant in (ii). So I went with one interpretation in my response. If you mean that to claim 'X is a paradox' is *itself* to make a really contradictory or paradoxical statement, I don't buy it, namely because it wasn't argued for.
ReplyDeleteIf your argument for how I'm interpreting it here was what you gave in (iii), then I take it the reason were sufficiently undermined.
So, the best I can read this interpretation is this:
[1] To claim, "X is a paradox" is to claim to know that X is not an actual contradiction.
[2] But to claim, "X is a paradox" is to not know that X is not an actual contradiction, for (*) if someone, S, knew X was a paradox then S would know it wasn't a paradox because X wouldn't appear contradictory anymore.
[3] (*) arises from affirming "X is a paradox."
[4] (*) is either a paradox or an actual contradiction.
[5] Therefore, if you claim "X is a paradox," then you either affirm an MAC or an AAC.
Is that close? I think [2] is obviously false.
Derek: Thanks very much!
ReplyDeleteSteve: I trust that you would agree that, using Paul M.'s nomenclature, your example wasn't a PUIMM. I don't have a problem with paradoxes of that sort. I also don't have a problem with my favorite "paradox": the apprenticeship in the Pirates of Penzance.
Paul M.: I would respectfully disagree with your view of what Clark would object to.
You asked: "Well, which is it? Have you seen no good reason why PUIMMs do exist or that they could or might exist?"
I have seen no good reason for any of "do" "could" or "might".
You argued: "Given (i), it would only be a paradox. Remember, you are supposing that there is a paradox that cannot be solved or reconciled before the bar of human reason."
!!
Are you sure you meant this?
You wrote: "Au contraire, mon frère ... " In this section you discussed how they can be distinguished.
With respect, however, this is self-defeating. If we can identify something as merely an apparent contradiction it is not a valid candidate for an apparent contradiction, unless we equivocate over what it means to be an "apparent" contradiction.
This the reason that I cannot imagine how the view of "paradox" in the PUIMM form could ever be demonstrated, because if we can distinguish it from a real contradiction, it no longer has all the appearances of a contradiction.
You wrote: "Yeah, this is just a non-sequitur."
I don't see how you can conclude that, especially in view of the shocking position (see the "!!") above.
You wrote: "You seem to be missing out on how strong of an argument you need to offer to deny the claim just expressed."
You seem to be limiting my options in terms of how I can go about in denying the claim that you expressed. In this case, I'm suggesting that any argument for PUIMM is necessarily self-defeating. If my argument is correct, then it is strong enough (although, apparently, you think it contains a non-sequitur, though you don't explain why).
As to your second comment, I am having trouble attaching your comment to my original argument. However, as best I understand it, your [2] is a position that I am taking (perhaps you will agree that I am taking that position in view of my comments above).
You say that you think [2] is obviously false, but you don't explain why. Perhaps you could assist me in understanding why you think that [2] is false and why you think there is a non-sequitur above (i.e. in your first comment of the two).
-TurreitnFan
TF wrote:
ReplyDelete"i) Suppose that there can be a paradox unable to be solved at the bar of human reason;"
"ii) Given (i), it would be either or a paradox or a real contradiction to say that there cannot be a paradox unable to be solved at the bar of human reason."
I don't see how (ii) follows from (i). What follows (trivially) from (i) is:
ii*) Given (i), it would be a falsehood to say that there cannot be a paradox unable to be solved at the bar of human reason.
A falsehood is not necessarily a paradox or a real contradiction. Why think that a denial of (i) generates either a paradox or a real contradiction?
I fear that TF's argument is founded on a blatant non sequitur.
For what it's worth, TF's (iii) is also false, as I explain in my book. It's perfectly possible to have rational grounds for believing that a particular paradox is a merely apparent contradiction. At any rate, TF hasn't given any argument for (iii). It isn't self-evident, after all.
Mr. Anderson:
ReplyDeleteWhy must it be false?
Isn't it false only if it is a contradiction? If it is a paradox, it is true, even though it appears to contradict (i).
-TurretinFan
TF,
ReplyDeleteSorry for the confusion. As I said, I didn't get your phrasing. So, when I said, "It's a paradox," I meant **the doctrine** is a paradox, *not* the *claim* that there is a paradox. My other interpretatio of your argument makes this reading of mine clear. So, the "shocking admission" was actually based on my not wanting to attribute the very bad argument (that I laid out below) to you.
"With respect, however, this is self-defeating. If we can identify something as merely an apparent contradiction it is not a valid candidate for an apparent contradiction, unless we equivocate over what it means to be an "apparent" contradiction".
With respect, this is just false. I explained partially how it could be that one can claim that X is apparently contradictory while not aparently contradictory.
Also, keep in mind the various positions. A *mere* apparent contradiction is an apparent contradiction but not an actual contradiction. So, "apparent contradiction" has *two* senses, which we agreed on way up there. If we can identify something as a MAC then it is not a candidate for an AAC, but it still is a candidate for an AC.
"This the reason that I cannot imagine how the view of "paradox" in the PUIMM form could ever be demonstrated, because if we can distinguish it from a real contradiction, it no longer has all the appearances of a contradiction".
With respect, I made arguments for the possibility of the claim and the extremely strongly counter-intuitive impression about man's mind you must be under. Again, you must be misunderstanding my argument. To defeat it, you must show that a paradox that remains irresolvable to humans is impossible.
"You seem to be limiting my options in terms of how I can go about in denying the claim that you expressed. In this case, I'm suggesting that any argument for PUIMM is necessarily self-defeating".
I'm not limiting anything. You're making a claim about impossibility. I'm asking you give an argument which can shoulder this burden. it is well-known the kind of argments that have to be made any time someone wants to claim an impossibility. If you are saying you have no argument for this, then you have no argument against the possibility of a paradox being irresolvable to man's mind.
"As to your second comment, I am having trouble attaching your comment to my original argument. However, as best I understand it, your [2] is a position that I am taking (perhaps you will agree that I am taking that position in view of my comments above).
You say that you think [2] is obviously false, but you don't explain why. Perhaps you could assist me in understanding why you think that [2] is false and why you think there is a non-sequitur above (i.e. in your first comment of the two)".
1. I gave a few reasons in my post. if you meant (iii) to back up [2], then I think I gave enough reasons to suppose (iii) untrue. Moreover, (iii) wasn't argument for. You seem to claim that (iii) does support my reconstruction of your position in [2].
2. James offered some reasons (directly) above.
3. [2] is obviously false because one can think some set of propositions, XY, are a MAC (via implicit contradiction) while also believing or knowing that XY is not a AAC.
If you don't think so, what would your argument be? (Again, note that A MAC would still be an AC while not being an AAC).
TF,
ReplyDelete"ii) Given (i), it would be either or a paradox or a real contradiction to say that there cannot be a paradox unable to be solved at the bar of human reason."
How's this: What would your argument be for the claim that "there cannot be a paradox unable to be solved at the bar of human reason?"
1. You have no argument. In which case, why should we accept your mere assertion?
2. If it is possible that there are irreconcilable paradoxes, then your claim would be false.
3. If you claim that "it is and it isn't" then it looks like we have an explicit contradiction going on, i.e.,:
The paradoxes of the trinity etc., are not like that. Looks like a perfect reason to reject your claim, just as if the trinity was: There is only one God. There is not only one God.
4. You are also supposing that if a person thinks a claim is a paradox he has no warrant whatever for claiming that it is not a actual contradiction. This wsas not argued for in the least.
So, your argument needs some work.
Sorry, I said:
ReplyDelete"With respect, this is just false. I explained partially how it could be that one can claim that X is apparently contradictory while not aparently contradictory."
It should be:
"With respect, this is just false. I explained partially how it could be that one can claim that X is [merely] apparently contradictory while not [actually] contradictory."
TF,
ReplyDeleteIn further response, as James agues in his book, there needs to be at least some possible distinctions on the terms so as to fulfill part of the constraints necessary for claiming we have a MACRUE.
If you want to claim that your claim is a paradox, can you parse out where some of the unarticulated equivocations lay?
If you want to affirm that it is an actual contradiction, then, per (i), it is *false*.
So, you cannot affirm that it *is* a contradiction, you must affirm that it is a paradox, if so, spell out some possible unarticulated equivocations.
TF, granting that (i) is true, it's denial does not look like a paradox at all. How is it paradoxical? I have no reason to believe it is true, unlike I do the various parts of Trinitarian doctrine. Paradoxes arises when you hold multiple propositions that you think are true, yet upon reflection they appear to contradict other truths. This doesn't look like the position: "There are no paradoxes that cannot not be reconciled before the bar of human reason."
ReplyDeleteSo, there's no reason whatsoever to believe it is a paradox. The reasonable position is that it is a contradiction. Since (i) is granted true, then it's denial must be granted false.
TF,
ReplyDeleteUnless I've badly misunderstood it, which is entirely possible, your argument is designed to show that the claim that there can be irresolvable paradoxes is itself a paradox.
Your premise (i) states your opponents' position, for the second of argument. Your (ii) then apparently tries to deduce some further proposition from (i) (since you say "Given (i)..."). What you deduce from (i) is that the negation of (i) (i.e., that there cannot be an irresolvable paradox) would be "either a paradox or a real contradiction".
But as I've pointed out, this is just a non sequitur. You've given no good reason to think this follows from (i).
Perhaps the idea is that, if irresolvable paradoxes are possible, then for just any proposition p we affirm, we must also be prepared to affirm non-p. But again, this is simply a non sequitur. It doesn't follow from (i) at all. Why think that it does?
One might as well argue that, if irresolvable paradoxes are possible, and we believe that the Earth orbits the Sun, then we should also be prepared to believe that the Earth doesn't orbit the Sun. The problem, of course, is that we have plenty of good reason to affirm the former and no good reason to affirm the latter. So your suggestion (if I read you correctly) that if the irresolvable-paradox view is true then it must (by its own lights) be on a par with the no-irresolvable-paradox view, begs the question entirely.
Correction: "non-p" should be "not-p".
ReplyDelete"I explained partially how it could be that one can claim that X is apparently contradictory while not aparently contradictory."
ReplyDeleteOne way would be by equivocating over what "apparently contradictory" means. I don't see another way. If that is the way, my original point stands.
UPDATE: I see, prior to my posting this, that you updated your comment to add the qualifiers "merely" and "actually." However, now I think you've missed the point, which related to things being both apparently and not apparently contradictory.
"With respect, I made arguments for the possibility of the claim and the extremely strongly counter-intuitive impression about man's mind you must be under. Again, you must be misunderstanding my argument. To defeat it, you must show that a paradox that remains irresolvable to humans is impossible."
You seem to have misunderstood my point, which was in regard to the attempts to provide examples of PUIMM. That is a separable issue from the issue whether or not an argument can be made that, although we cannot provide any examples, there must (or at least could) be one out there. That sort of argument falls in a different category and requires a different sort of response.
"I'm not limiting anything. You're making a claim about impossibility. I'm asking you give an argument which can shoulder this burden."
You're asking my argument to take a particular form. I would respectfully submit that there is more than one way to skin a cat.
"... because one can think some set of propositions, XY, are a MAC (via implicit contradiction) while also believing or knowing that XY is not a AAC."
This supports my position rather than contradicting it. Let me explain:
a) By definition a MAC is a merely apparent contradiction.
b) By definition an AAC is both an apparent contradiction and an actual contradiction.
c) If we say we think something is a MAC, we are saying at the same time that we think it is not an AAC.
d) However, if we can establish that something is not an actual contradiction, it no longer appears to be a contradiction, unless (of course) we equivocate over the meaning of "apparent."
***
"How's this: What would your argument be for the claim that "there cannot be a paradox unable to be solved at the bar of human reason?""
You seem a bit off-track here.
1) My item (ii) is just asking you the reader to acknowledge that vis-a-vis item (i), the directly contrary assertion is either (a) a contradiction of (i) or (b) a paradox (or 1/2 of the paradox ... the two being in paradoxical relation) that is not a contradiction of (i) but merely appears to be.
"2. If it is possible that there are irreconcilable paradoxes, then your claim would be false."
It appears you are assuming that the law of non-contradiction applies to this instance.
"3. If you claim that "it is and it isn't" then it looks like we have an explicit contradiction going on, i.e.,:"
Yes. And only if the law of non-contradiction applies is that a problem.
"The paradoxes of the trinity etc., are not like that. Looks like a perfect reason to reject your claim, just as if the trinity was: There is only one God. There is not only one God."
I'm certainly not arguing against the Trinity, and I don't see any apparent contradictions involved in Trinitarian doctrines.
There are certainly mysterious aspects to the Trinity that fall into the category of things we just don't know because we haven't been told. On the other hand, I see nothing that would make me think that there is any contradiction. Perhaps, however, that is because I tend not to view things as "contradictions" when they cannot be recast into a "X is true" "X is not true" format with a little ingenuity.
"4. You are also supposing that if a person thinks a claim is a paradox he has no warrant whatever for claiming that it is not a actual contradiction. This wsas not argued for in the least."
No, you've misunderstood me. I agree that if a person is claiming something is a MAC he has [or at least ought to have] warrant for thinking it is not an AAC.
***
FURTHER UPDATE: Every time this response is ready to post, there is something new.
"So, you cannot affirm that it *is* a contradiction, you must affirm that it is a paradox, if so, spell out some possible unarticulated equivocations."
a) If I spell them out, how would they be unarticulated?
b) More importantly, if there is identifiable equivocation going on then the appearance of contradiction is lost. Let me provide a simple example:
Steve is the most wily of the Reformed bloggers.
Mr. Hays is the most wily of the Reformed bloggers.
I understand that this might seem to someone at first to sound like competing claims for wiliness. In fact, however, as we know, there's sort of a reverse equivocation going on here, since both "Steve" and "Mr. Hays" are names of the same guy.
We could see actual equivocation in the following:
Steve is the most wily of the Reformed bloggers.
Steve is NOT the most wily of the Reformed bloggers.
Here the equivocation is that I am referring to Mr. Hays in the first one and Mr. Camp in the second one (no offense, brother Camp). Maybe, without clarification they look contradictory (they even look directly contradictory) but with clarification they can be seen to be consistent.
Notice how, by identifying the equivocation I destroyed the appearance of contradiction.
***
James mentioned: "Perhaps the idea is that, if irresolvable paradoxes are possible, then for just any proposition p we affirm, we must also be prepared to affirm non-p."
Yes, on its face, if somehow we gain knowledge that irresolvable paradoxes are possible, then for any proposition p, we must also be preared to affirm non-p. The way out of that would be to also somehow gain knowledge that paradoxes are only possible within a specific realm of knowledge (and then, to avoid the same argument above, that this specific realm does not include either the general proposition that there are such paradoxes or the more narrow proposition that the realm does not include either the general proposition or the ...).
Now, I understand from Paul's claim that you are making a further claim that not only are paradoxes (of the irreconcilable type) possible but also that they can only occur with respect to the Trinitarian doctrines (or something like that).
But frankly, the more limited this acceptance of paradox is, the more and more it looks like it is being created simply to avoid having to resolve the apparent contradictions.
-TurretinFan
Hi TF,
ReplyDelete"UPDATE: I see, prior to my posting this, that you updated your comment to add the qualifiers "merely" and "actually." However, now I think you've missed the point, which related to things being both apparently and not apparently contradictory".
To make this argument you need to prove:
[1] A set of propositions, XY, cannot appear to be a mere contradiction and not appear to be an actual contradiction.
I will await your argument for [1].
"You seem to have misunderstood my point, which was in regard to the attempts to provide examples of PUIMM. That is a separable issue from the issue whether or not an argument can be made that, although we cannot provide any examples, there must (or at least could) be one out there. That sort of argument falls in a different category and requires a different sort of response".
Let's make this simple:
a) I am affirming that it is possible that there could be paradoxes irresolvable by the bar of human reason.
b) You are affirming ~(a).
I argued for (a), that is, made claims that it is possible that there could be such paradoxes. To defeat (a) you need to show that it is impossible. I have not seen that argument yet. That’s the only way to do it. There’s only one way to skin this kind of cat. You also need to defend the hidden premise that no metaphysical distinctions could be so complicated that a finite mind could not grasp them.
"You're asking my argument to take a particular form. I would respectfully submit that there is more than one way to skin a cat".
You are simply mistaken here. You cannot claim that p is impossible with an argument that doesn't lead to that conclusion. I am not asking for a specific "form." I am making a basic philosophical point.
I wrote: "... because one can think some set of propositions, XY, are a MAC (via implicit contradiction) while also believing or knowing that XY is not a AAC."
You responded:
"This supports my position rather than contradicting it. Let me explain":
No it doesn't, but I'll let you explain.
"a) By definition a MAC is a merely apparent contradiction".
Right; merely apparent, but still apparent.
"b) By definition an AAC is both an apparent contradiction and an actual contradiction".
Right.
"c) If we say we think something is a MAC, we are saying at the same time that we think it is not an AAC".
Right.
"d) However, if we can establish that something is not an actual contradiction, it no longer appears to be a contradiction, unless (of course) we equivocate over the meaning of "apparent".
We just went in a big circle. There is no equivocation on "appear." If I know that XY only appear to contradict while not actually contradicting, then XY still appear to contradict. I'll wait for your argument showing otherwise.
I wrote:
"How's this: What would your argument be for the claim that "there cannot be a paradox unable to be solved at the bar of human reason?"
You responded:
"You seem a bit off-track here".
I'm not. :-)
"1) My item (ii) is just asking you the reader to acknowledge that vis-a-vis item (i), the directly contrary assertion is either (a) a contradiction of (i) or (b) a paradox (or 1/2 of the paradox ... the two being in paradoxical relation) that is not a contradiction of (i) but merely appears to be".
I have no reason to view it as a paradox. Paradoxes arises for subjects. If I have no reason to believe that not-(i) is true, then I have no reason to believe that not-(i) is paradoxical conjoined with (i). I only have reason to believe that it is a contradiction.
I wrote:
"2. If it is possible that there are irreconcilable paradoxes, then your claim would be false."
You responded:
"It appears you are assuming that the law of non-contradiction applies to this instance".
Yeah, and? I'm (honestly) not following how these moves are supposed to work in your favor.
I wrote:
"3. If you claim that "it is and it isn't" then it looks like we have an explicit contradiction going on, i.e.,:"
You responded:
"Yes. And only if the law of non-contradiction applies is that a problem".
Defenders of paradox do not deny the law of non-contradiction.
I wrote:
"The paradoxes of the trinity etc., are not like that. Looks like a perfect reason to reject your claim, just as if the trinity was: There is only one God. There is not only one God."
You responded:
"I'm certainly not arguing against the Trinity, and I don't see any apparent contradictions involved in Trinitarian doctrines".
You missed the point. You offered a crass explicit contradiction. That's reason enough to reject your appeal to "paradox" to as a possible explanation for not-(i).
"No, you've misunderstood me. I agree that if a person is claiming something is a MAC he has [or at least ought to have] warrant for thinking it is not an AAC".
This makes a concession in my favor, it would appear. You admit that a person can claim that XY is merely apparently contradictory while not an apparent and actual contradiction.
I wrote:
"So, you cannot affirm that it *is* a contradiction, you must affirm that it is a paradox, if so, spell out some possible unarticulated equivocations"
You responded:
"a) If I spell them out, how would they be unarticulated"?
You missed the word 'possible' in my post. To claim something is a MACRUE (one of your possible explanations for not-(i)), you need to offer some possible areas of unarticulated equivocations. They may not be actual, but not being able to think of any means more of a problem claiming that XY are MAC rather than AAC. Furthermore, you need to offer an implicit rather than crassly explicit contradiction.
The rest of your points after this were based on your misunderstanding of what I asked you t provide.
So, I think I've defended both these positions:
(a) Your [2] is obviously false as it is based on misunderstandings, mischaracterizations, and non-sequiturs.
(b) You have not shouldered your burden by offering an appropriately strong argument to attend your strong claim of impossibility, while I have offered as-of-yet undefeated reasons for thinking an irresolvable paradox could be possible, even if none are actual.
TF,
ReplyDelete"But frankly, the more limited this acceptance of paradox is, the more and more it looks like it is being created simply to avoid having to resolve the apparent contradictions".
In all sincerity, if this is what your argument is ultimaely reduced too, then you have failed to show that it is impossible that such a paradox could exist. Making the ad hominem comment about motives doesn't count, in the slightest, to defeat the claim that an irresolvable at the bar of human thinking is possible.
Turretinfan said...
ReplyDelete"Steve: I trust that you would agree that, using Paul M.'s nomenclature, your example wasn't a PUIMM. I don't have a problem with paradoxes of that sort. I also don't have a problem with my favorite 'paradox': the apprenticeship in the Pirates of Penzance."
i) I'm unclear on your restricted appeal to the law of non-contradiction. You seem to think it precludes the possibility of some apparent contradictions, but not others. Yet it's a universal law. So if it's relevant to apparent contradictions at all, why wouldn't it either apply to all apparent contradictions or no apparent contradictions?
ii) In addition, professional logicians often generate logical paradoxes. If even logicians can generate logical paradoxes, some of which are highly resistant to resolution, how does the law of non-contradiction ipso facto preclude certain apparent contradictions?
TF,
ReplyDeleteI think I have an argument you will find persuasive.
Above you said:
"There's only a particular form of "paradox" to which I object".
I said Clark wouldn't be happy. You disagreed. Presumably, you think it acceptable to believe a paradox so long as it is reconcilable. You certainly haven't tried to argue that no one may ever be rational in believing any paradoxical set of claims whatever.
So, I think we're in agreement so far.
However, you have wanted to claim something like this "If You Can Tell" principle:
[IYCT] = If someone, S, can tell that a set of propositions, XY, is merely apparent contradiction, then XY will not apear contradictory.
Now, say you believe that a set of propositions, XY1, are a paradox.
To believe that, you would have to believe that XY1 merely appear to contradict. This would mean that XY1 would not appear to contradict (per your own [IYCT] premise). This would mean that XY1 would not be paradoxical since it is analytic that a paradox at least appear to contradict (according to [IYCT]).
Furthermore, since you can't tell the difference between a paradox and and actual contradiction (on your own premises, and if you deny this you deny your entire argument), you don't know that XY1 would ever be resolved. You don't know that XY1 is not an actual contradiction. If you knew it would be resolved you would know it was not an actual contradiction, but then, it wouldn't appear to contradict anymore, per your [IYCT], and so it wouldn't be a paradox.
Since this argument, built strictly from your premises, seems to force you to deny what you specifically affirmed, you ought to deny your present argument.
If you don't, then you need to argue that it is epistemically naughty to believe any paradox, irreconcilable or not. That makes your already difficult task of arguing for the impossibility of an irreconcilable paradox, even harder.
Paul:
ReplyDeleteI think we must be talking past each other. You wrote that I must prove: "[1] A set of propositions, XY, cannot appear to be a mere[ly] [apparent] contradiction and not appear to be an actual contradiction."
Even assuming I've correctly edited your comment, there's a double negative in there.
I think you are trying to claim that I have to prove that every merely apparent contradiction (MAC) must also appear to be an actual contradiction (AC). If so, I'm at a loss for words. How can something be a MAC unless it appears to be an AC?
Steve: No, I think it's a universal law, and therefore precludes only irreconcilable paradoxes. The "paradox" of Hays vs. Steve or "Steve [hays] vs. Steve [camp]" is reconcilable (some sort of equivocation or reverse equivocation was involved) and consequently they are not problematic. Basically, I'm objecting to the idea that truth ever violates the Law of Non-contradiction without equivocation being involved.
-TurretinFan
As for the IYCT argument ... you seem to mistake the impact of the argument. The impact is that - as I said - the only way to call the original situation a MAC is to equivocate over the sense of "appear."
ReplyDelete-TurretinFan
"Making the ad hominem comment about motives doesn't count, in the slightest, to defeat the claim that an irresolvable at the bar of human thinking is possible."
ReplyDeleteI know and I agree, at least in the main. I'm just letting you know I'm getting suspicious.
-TurretinFan
TURRETINFAN SAID:
ReplyDelete“Steve: No, I think it's a universal law, and therefore precludes only irreconcilable paradoxes. The ‘paradox’ of Hays vs. Steve or "Steve [hays] vs. Steve [camp]" is reconcilable (some sort of equivocation or reverse equivocation was involved) and consequently they are not problematic. Basically, I'm objecting to the idea that truth ever violates the Law of Non-contradiction without equivocation being involved.”
Thanks for the clarification. However, as an objection to folks who make allowance for paradox, isn’t that a straw man? It’s not as if they think truth violates the law of non-contradiction. As I’ve said before, this is not about the nature of truth, but the perception of truth. A relation between the subject of knowledge and the object of knowledge. It still is unclear to me why you think reality is sufficiently transparent to the finite mind of man that no truth would ever seem impenetrably paradoxical. Since, where the mind of man is concerned, in contradistinction to the mind of God, the object of knowledge is frequently more complex than the subject of knowledge, I find your antecedent expectation difficult to justify.
Reality as a whole will always be more complex than the human mind. And various subsets of reality will always be more complex than the human mind.
TF,
ReplyDeleteI don't know how else to spell it out for you, I'll make one more try (and I think I showed some serious problems with your argument in my post above the one your responded too, oh, and my "double negative" sentence made sense...anyway).
You claimed that:
"d) However, if we can establish that something is not an actual contradiction, it no longer appears to be a contradiction, unless (of course) we equivocate over the meaning of "apparent".
To believe that a set of claims is a paradox is to believe that it appears contradictory. Right?
But if you believe that you can rationally believe that something is a resolvable paradox, this means that you "establish[ed] that that something is not an actual contradiction." From here it follows, strictly from premises you've affirmed, that the something "no longer appears to be a contradiction, unless (of course) we equivocate over the meaning of 'apparent'. But from this it follows, again, strictly, that you no longer believe that something is a paradox because you no longer believe that something appears contradictory, and a minimum requirement for a paradox is that it appear contradictory.
Therefore, your own argument requires you to deny something you've affirmed.
See, you agreed with [2] above. To remind you, [2] was:
"[2] But to claim, "X is a paradox" is to not know that X is not an actual contradiction, for (*) if someone, S, knew X was a paradox then S would know it wasn't a paradox because X wouldn't appear contradictory anymore".
But if you believe that you can believe in paradoxes now, and you do, then you must deny [2].
Is that more helpful?
Turretinfan said...
ReplyDeleteAs for the IYCT argument ... you seem to mistake the impact of the argument. The impact is that - as I said - the only way to call the original situation a MAC is to equivocate over the sense of "appear."
-TurretinFan
5/02/2009 6:25 PM
You keep saying that, you haven't shown it. Indeed, I have no clue what you're even trying to get at by saying it.
Turretinfan said...
ReplyDelete“But frankly, the more limited this acceptance of paradox is, the more and more it looks like it is being created simply to avoid having to resolve the apparent contradictions".
"[Manata] Making the ad hominem comment about motives doesn't count, in the slightest, to defeat the claim that an irresolvable at the bar of human thinking is possible."
“I know and I agree, at least in the main. I'm just letting you know I'm getting suspicious.”
Since you introduced the issue of ulterior motives, let’s address that charge:
On the one hand:
i) It’s true that appeal to paradox has the potential, when abused, of degenerating into special pleading. The theologian can always play his get-out-of-jail card.
ii) By the same token, appeal to paradox can also become addictive. The path of least resistance. We don’t even try to understand something difficult.
On the other hand:
i) Opponents of paradox can have ulterior motives as well. For example, they may reject paradox because they think it leads to practical problems or unacceptable consequences, like the (alleged) inability to distinguish between a real contradiction and a merely apparent contradiction.
ii) In addition, one can be motivated to reject paradox on liberal as well as conservative grounds. Samuel Clarke rejected paradox. He regarded the Trinity as paradoxical. Hence, he rejected the Trinity.
Finally, permit me to make an autobiographical observation. I don’t find the paradigm-cases of theological paradox all that impressive.
(Mind you, I think it takes some hard thinking to work through these issues.)
Ironically, I’m open to theological paradox, not because I have a theological agenda, but because I encounter so many cases of paradox outside theology–in logic, mathematics, and the sciences. That being the case, I wouldn’t expect theology to be exempt from paradox.
[TF]: “But frankly, the more limited this acceptance of paradox is, the more and more it looks like it is being created simply to avoid having to resolve the apparent contradictions".
ReplyDelete[Manata]: Making the ad hominem comment about motives doesn't count, in the slightest, to defeat the claim that an irresolvable at the bar of human thinking is possible."
[TF]: “I know and I agree, at least in the main. I'm just letting you know I'm getting suspicious.”
I'd just add that James Anderson looks at numerous resolutions in his book (and those are just the ones he chose to spotlight), so it's hard to claim that there's a desire to avoid finding resolution. In fact, Anderson is always looking for possible resolutions to doctrines he takes to be paradoxical. One impression his book gives you is that he's left no stone unturned in search for orthodox resolutions.