Sunday, January 15, 2012

Infinite Worldviews

According to John Robbins:

In the laboratory the scientist seeks to determine the boiling point of water. Since water hardly ever boils at the same temperature, the scientist conducts a number of tests and the slightly differing results are noted. He then must average them. But what kind of average does he use: mean, mode, or median? He must choose; and whatever kind of average he selects, it is his own choice; it is not dictated by the data. Then too, the average he chooses is just that, that is, it is an average, not the actual datum yielded by the experiment. Once the test results have been averaged, the scientist will calculate the variable error in his readings. He will likely plot the data points or areas on a graph. Then he will draw a curve through the resultant data points or areas on the graph. But how many curves, each one of which describes a different equation, are possible? An infinite number of curves is possible. But the scientist draws only one. What is the probability of the scientist choosing the correct curve out of an infinite number of possibilities? The chance is one over infinity, or zero. Therefore, all scientific laws are false. They cannot possibly be true. As cited above, the statement of Karl Popper is correct: "It can even be shown that all theories, including the best, have the same probability, namely zero."

Many popular Scripturalists have taken this quote and run with it (link, link). For the sake of this post, I am not interested in the argument so far as it criticizes empiricism. My interest lies in the idea that if one must choose from an infinite number of alternatives, his chance of correctly choosing is zero. Let's apply this to the following statement made by Vincent Cheung, a Scripturalist who agrees with the above reasoning:

For every truth, there is logically an infinite number of possible falsehoods related to it or deviations from it. For example, if the truth is 1 + 1 = 2, then, we can deviate from this by saying 1 + 1 = 3, or 4, or 5, or 6, and so on to infinity. This is the case regarding any truth. (link)

If there are an infinite number of possible falsehoods, then consider this analogy:

In the search for truth, an epistemologist will encounter an infinite number of possible worldviews. But the epistemologist chooses only one. What is the probability of the epistemologist choosing the correct worldview out of an infinite number of possibilities? The chance is one over infinity, or zero. Therefore, all epistemological choices of worldviews are false. They cannot possibly be true. As cited above, the statement of Karl Popper is correct: "It can even be shown that all theories, including the best, have the same probability, namely zero."

A few implications from this line of reasoning:

I don't think it's the case that just because one chooses one alternative out of an infinitude of alternatives, his choice is necessarily false. I disagree with Robbins argument, or at least the reasoning he used to reach it. Perhaps a scientific law cannot be know to be true, but certainly not all scientific laws would be false simply due to the presence of an infinite number of false scientific laws.

Furthermore, in the context of epistemology, if it can be shown that the unique characteristics of a given worldview are necessary preconditions for knowledge, then that worldview would be both true and knowable. And assuming a certain view of mathematics, one can use transcendental arguments to refute an unlimited number worldviews, as I point out here.

Speaking of mathematics, the more I study divine omniscience and epistemology, the more striking its importance appears. I'll admit that it's hard for me to wrap my head around it.

Clark would probably avoid this whole discussion by arguing that there are only a finite number of possible worldviews, and this of course has significant implications regarding mathematics. But it doesn't seem to me that Clark had a very good grasp of mathematics. This is just a guess based on an anecdote in Gordon Clark: Personal Recollections, but I think he probably rejected the concept of infinite knowledge soon after he was shown that not all infinite sets are countable.

At any rate, I suspect that a form of mathematical induction - which is actually deductive (link) - could possibly be used to refute what might be called trivially similar and impragmatic worldviews, especially ones centered on [a] number(s).


otto said...

Hi Ryan,

I was your opinion, did Clark believe in a (i shudder to say the words) finite God???

otto said...

Sorry, I guess that was a little off topic.

Ryan said...

Clark would want a precise explanation as to what [in]finitude is.

Clark denied that God's knowledge could be "infinite" because he thought such implies that God's knowledge would be unbounded; the extent of what could be known would be more than the mind could contain.

On the other hand, Clark did not believe anything external to God could limit or condition God's eternal decree.

otto said...

Clark did not believe anything external to God could limit or condition God's eternal decree."

I get this.

So now, God has a Mind which knows All. But this "all" is still bound in God's mind. Do I understand this correctly? That would be Clark's view?

And what if I were to say that God's knowledge really is unbounded, and for instance, it corresponds with the "no last term." So God's knowledge would still be omniscient because it would always be in-sync (for lack of better word) with the "ongoing" last term? What do you think of that? Although that makes it kind of mutable, right?

It just seems to me that saying "infinity has no last term" isn't that great of a definition for infinity. I certainly do not have a better one! But then again, how would one define eternity? Do you know how Clark defined eternity?

And do you agree with Clark on his point of infinity? Or do you have another view to posit (since you are studying this stuff)

Thanks for that concise explanation.

Ryan said...

Clark thought that to know "all" by definition meant to know a finite number of propositions; if there isn't any limit to the number of knowable propositions, then to say God knows "all" is simply a misunderstanding of what "all" means.

Clark essentially equated eternity with immutability (link).

As for myself, I am undecided. While I recognize Clark's concerns, if he did not know as much about higher level math as is implied by his ignorance of uncountable sets alluded to in Gordon Clark: Personal Recollections, I am at least not willing to use Clark's arguments as to arbitrate of my beliefs in this matter. The Cantor set, for example, is a set which is uncountable yet bounded, so it could be the case that some analogy can be made between this and an infinitely knowledgeable God. It is a point I have been meaning to study but haven't had the time to.

otto said...

Thanks for the link.

So in Clark's view God knows every proposition. And would it be ok to say that ALL the propositions are in God's mind? (all the finite propositions i guess? or am i wrong here)

Im going to read through the time and eternity article tomorrow, also looking forward to see what you have to say regarding the Cantor set when you get around to it.

Can you give me the pagination for Personal Recollections wherein it speaks of Clark and uncountable sets?

Ryan said...

Yes, that would be Clark's position.

I don't have the book with me but should be able to post it tomorrow.

Ryan said...

William Young in Gordon Clark: Personal Recollections (pg. 117) wrote:

Once at a luncheon, he was pointing out that there is a one-to-one correspondence between the members of the set of even integers and all the integers, and concluded that there was only one infinity. I mentioned Cantor's diagonal proof that the number of decimals between 0 and 1 is an infinity larger than can be brought into such a correspondence with the integers. Clark replied: "I am silenced, but not convinced."

otto said...

Very interesting. I did not notice that when I rented and read Personal Recollections. Thanks.

MikeD said...

As for Robbins' assertion that all laws of science are false, I would agree that perhaps the proposition is, in fact, one that God thinks, thus true, and in that case would be at least correct opinion on our part. Presumably we'd find out in glory. But I've always seen Robbins here speaking ad hominem. Namely, given their probabilistic calculus for the determination of truth, scientist would need to say that the probability of the truth of the law is basically zero and not worthy of assent. Incidentally, this comes from no inordinate desire to keep anybody in the right, but as I'm sure you are well aware, especially with Clark, he often had the habit of forgetting to let the reader know when he was walking us through another's point of view and when he was back to his own thoughts.

A quick one for you: if one assented to natural law x, and that happened to be a proposition of God's mind, would you say that the person had knowledge?

Lastly, as of it was a small undertaking, I'd love to hear your thoughts on divine simplicity even if nothing other than a brief commentary on the recent interview with James Dolezal on Reformed Forum. Cheers.

Ryan said...

My problem is not with the statement that scientific laws are false per se, my problem is with the reasoning Robbins' uses to arrive at that conclusion:

"What is the probability of the scientist choosing the correct curve out of an infinite number of possibilities? The chance is one over infinity, or zero. Therefore, all scientific laws are false."

To answer your questions:

No, that person would not have knowledge.

I'm not aware of the interview you are referring to. Do you have a link?

MikeD said...

Here's the link for the Christ the Center episode discussing simplicity:

James Dolezal also just recently published a book on the subject. While I'm not aware that Clark ever spoke directly to the subject, by name at least, I would have thought that he would repudiate a strong Thomistic view of simplicity that seems tantamount to nominalism and analogical predication Apparently I was wrong as indicated on p.64 @ the end of section 7 of The Incarnation.

Ryan said...


Thanks. I'll listen to it tomorrow, as it's pretty late here. I know of a few additions to your citation of Clark on divine simplicity:

From an excerpt of his book The Atonement:

"Augustus Toplady wrote, among other things, “Observations on the Divine Attributes.” The simplicity of God and the identity of all the divine attributes, used above to settle the relation between justice and sovereignty, Toplady expresses in the following words. “Although the great and ever blessed God is a Being absolutely simple ... he is, nevertheless, in condescension to our weak and contracted faculties, represented in Scripture as possessed of divers properties, or attributes, which though seemingly different from his essence, are in reality essential to him, and constitutive of his very nature” (p. 675, col. 1). Toplady, then, specifies “his eternal wisdom, the absolute freedom and liberty of his will, the perpetuity and unchangeableness, both of himself and his decrees, his omnipotence, justice, and mercy.”

The material is so good that it demands great restraint not to quote the entire article, twelve pages of long double columns."

I have his ebook on The Trinity in ebook format, and he speaks about it there as well in clearer terms (chapter titles in parentheses):

"Chapter V, paragraph 22 reads as follows.

If then any man conceives as if God were compound, so as to have accidents in his substance,...or as if there is ought about him that completes his substance, so that when we say “God,” or name “Father,” we do not signify the invisible and incomprehensible substance, but something about it, then let them complain of the Council’s stating that the Son was from the substance of God; but let them reflect that thus considering they commit two blasphemies; for they make God material, and they falsely say that the Lord is not Son of the very Father, but of what is about him. But if God is simple, as he is, it follows that in saying “God” and naming “Father,” we name nothing as if about him, but signify his substance itself.

Some more recent theologians, seen in the Reformed tradition, assume that there are attributes, essentially or definitionally different from each other, somehow inhering in a nondescript, quality-less, unknowable substance. Athanasius makes the attributes, the substance, and God identical." (Athanasius)

"Orthodoxy maintains that the Three Persons are equal in power and goodness. Indeed Being and Goodness are identical. But Eunomius destroys the simplicity of God, and while he holds that the Being of the Father is “Supreme and Proper,” he refuses these titles to the Son." (Three Intermediates)

"Augustine is confused in chapter V when he says that if predicates exist in a subject, God, being simple, can have no predicates. He then concludes that God is not a substance but an essence, though earlier he had made these terms synonymous. Indeed, he asserts that “God alone should be called essence.” This would mean that neither cacti nor triangles could be defined." (Augustine)

"If God’s knowledge is not demonstrative, he must be ignorant of the Pythagorean theorem. He did not have to labor, as Pythagoras did, to discover the proof, but still it is a demonstrative proof and God knows the demonstration. Nor can we agree with Berkhof when in the same paragraph he maintains that some parts of God’s knowledge are and some are not “purely an act of the divine intellect without any concurrent action of the divine will.” This radical separation of the will from the intellect is destructive of the simplicity of the divine nature. And, further, it would seem to require alternating periods of time when the will was active and the intellect was not with other periods when the reverse was the case. This is inconsistent with God’s eternity." (Hodge and Berkhof)

Ryan said...

Quickly, a few comments on [late] Clark's view of simplicity:

He equated all the divine attributes, something with which I would disagree. While demolishing the walls of Jericho may have demonstrated [both] God's grace and wrath, this is not evidence that God's grace is His wrath. I don't find that to make any sense, and I find it puzzling why someone of Clark's intelligence would think that.

I do agree with Clark in a few respects. Firstly, he never subscribed to a Plotinian theory of divine simplicity. That is evident in the quote I provided from his chapter on Augustine in The Trinity. Secondly, I agree with Clark on the necessity of all God's works (creation et. al.), which some seem to think has a bearing of the doctrine of simplicity. And obviously I reject that God has a bodily composition, so I guess that can be a way in which God is simple.

I think God's knowledge is complex in the sense that it is synthetic. This is not to say that I reject any formulation of divine simplicity nor to say that God's knowledge is discursive, but God knows more than one truth. He knows a complex of truths. I think this is a useful point to remember when accused of regarding a causal correlation between divine nature and will as implying "absolute" (if you will) divine simplicity.

This may address some of what you wanted my opinion about regarding the discussion with Dolezal.

MikeD said...

Thanks for the thoughts and the footwork regarding the Clark quotes... very helpful. I recently read Clark say something to the fact that the number of angels created could not have been different and I take this to similar to your sentiment as per your statement regarding the necessity of creation. For a long time now I've enjoyed the strength of notion that this is the best world seeing that it is the very world he hath willed. He must and will glorify himself perfectly, thus there is a necessity to this world.

Perhaps this is not the forum for confession of a sort, but when approached from that angle, I would concur with you. When approached from the vantage point of thinking that God would not be God had I not been bit by that mosquito last night, the thought bothers me a bit. Is it not possible that so-called Cambridge properties, or perhaps stronger accidental properties, can alleviate having to say that there is a one-to-one existence between the great I AM and the truth of how many hairs were on my head at the time I typed this comment?

Thanks again for your time and I think you'll agree after listening to the stimulating episode of Christ the Center that a strong doctrine of simplicity is not needed to preserve the sovereignty-aseity teaching of scripture. Biblical realism is plenty without the loss of univocal predication to boot. While I'm not normally interested in the name game, those that constantly defend Van Til from the accusation that he takes Thomas' doctrine of analogy need to listen to this episode and see the intimate connection between analogical predication and simplicity. Hodge says rightly that if the differences spoken of in Scripture are only differences of effect or in our consciousness, the knowledge of God is destroyed and we use words which have no meaning.

Ryan said...

An immediate question that came to mind when reading your example is, "what would constitute a Cambridge property and how would you know?" Is it not the case that an event which may seem irrelevant to oneself at one point in the future be demonstrated to be relevant and, if not, how do you know?

Furthermore, if such events aren't necessary, is not God's ordination of them arbitrary? I would rather plead ignorance as to how these events function as a means to the maximal manifestation of God's glory than entertain the alternative.

MikeD said...


As noted before I have an affinity for the proposition that all of God's works are necessary, but as I work through the subject I was wondering how you would deal with the following ideas:

(1) If what is actual is not a subset of what is possible, but rather equal, then how would we explain Matt 3:9 and Matt 26:53? In the former, the Father could turn those stones into children of Abraham, but he chose not to. In the latter, the Father could send legions of angels to do thus and such but he did not. I know Clark has several statements expressing the notion that this is the only possible world, but the above verses comport with his sentiment from Predestination (p.41 - "Omniscience") which reads as, "What God calls and chooses is not unknown to him. Thus he knows what is possible, whether or not he ever makes it actual."

(2) As to your question about the arbitrariness of the divine will, if indeed there is some type of non-necessity of God's decrees, I would also defer to Clark from his commentary on Ephesians (p.20-21). Two out of three of the definitions listed fit exactly with the teaching of Scripture. That is to say, it is literally despotic and of the will, but not capricious and random or without purpose.

Thanks again for your fine thoughts and study.


Ryan said...

Hello again MikeD.

As for (1), I accept that Clark's position evolved over time. Later in life he accepted the necessity of this possible world (link). I would say that those and any other similar passages can be taken in the way Paul Helm mentions in Eternal God, pgs. 188-189:

"...there is a difference between saying that a state of affairs is internally consistent quite apart from the question of whether it is possible that God would actualize it and saying that it is possible that God would actualize it. If the question, 'Could God have instantiated a world different from the actual world?' is a question about God's power then the answer must be that if it is a consistent state of affairs then God's power could have actualized it. But that God is sufficiently powerful that he could is not to say that he would. In fact, we know from the actual world that he would not, because he has not. Abstracted from God's will such consistent alternatives are possible... But if we were to know everything, or more than we do, then we would see that these possibilities are only abstract. They do not represent real possibilities and never did."

In essence, they can be viewed as hyperbolic. They serve for a rhetorical effect.

As for (2), if God has a reason for ordaining what he has, then either the reason was necessary or unnecessary. If necessary, then this is the only possible world. If unnecessary, then the "reason" itself is willed arbitrarily. I mention this in point 1 of this post.