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).

Knowing Truth: Related or Isolated?

In my last post, I mentioned the doctrine of internal relations as implying the necessity of an eternally omniscient being. I've written about this necessity before (most comprehensively, here). The doctrine of internal relations is the theory that everything is related to everything else. "Everything," however, may be unnecessarily ambiguous, so let's qualify it to specifically apply to propositions. Are all propositions related, or can a proposition be known to be true in isolation from all others?

By definition, one who isn't omniscient doesn't know at least one proposition: A.

For such a person to claim to know proposition B is false if B is predicated on A.

For him to know that B is not predicated on A presupposes a method C according to which he is able to determine such.

The question, then, becomes: from whom did he learn C, or did he himself claim to discover it?

If one learned C from another, from whom did that person learn C, did that person claim to discover C, or is that person omniscient?

If that person in turn learned C, we merely repeat the same question such that it is evident one has discovered C himself or has ultimately learned C either from one who is not omniscient and claimed to have discovered it or from one who claims to be omniscient.

Here is the kicker: if either of the former is the case - if a non-omniscient source claimed to discover C - by what method D did said source discover that C is not itself predicated on A? By what method E did said source discover that D is not itself predicated on A? Etc.

It is apparent that one who is not omniscient cannot both claim to know a proposition in isolation and avoid begging the question. Note that this is not intended to question the right of a person to appeal to an epistemic source. It is rather a question of determining preconditions for [the means of] knowledge and whether or not a particular epistemic source satisfies them. This post, like the one cited at the top, is intended to establish the unviability of an epistemology which has no recourse to an omniscient source of knowledge. The point is that just as no epistemology can stand without logic, no epistemology can stand without an omniscient being - more precisely, an eternally omniscient being, if the argument in my other post is sound. I'll leave that aside for now, however, as I want to emphasize that I believe this is a strong argument against secular rationalists who believe logic alone is a sufficient condition for knowledge. It's the best one I know, anyway, in terms of its breadth of application.

Clark, Van Til, and the Knowledge(s) of Man and God

I have yet to see a more fascinatingly concise, if perhaps equivocal, assessment the Clark-Van Til controversy on the issue of how the knowledges of man and God relate than that provided by Robert Rudolph in his contribution to Gordon Clark: Personal Recollections (pgs. 103-104):

Gordon was absolutely insistent that we did know some of the same things that God knew. If not, he insisted, it would be impossible for us to know any truth at all! That 2 plus 2 equals 4 is true, he felt. Thus he insisted that in and of itself it is true as a statement without the necessity of examining another proposition. He carefully insisted upon a propositional concept of truth while Van Til insisted upon the fact that to have truth in one's mind that mind must be built upon other propositions. The truthfulness or falsity demanded that the individual proposition be held in the midst of certain other basic propositions that must be consciously present in that mind in order to correctly know truth. Now, of course, God knows every proposition in the context of all other propositions for Van Til, and, therefore, the limited human mind never knows it the way God does. Van Til had an expression, of repeated: "true as far as it goes," meaning, of course, that for that mind which holds all propositions in a system, the more complete the system, the more full the truth. With growth in the knowledge of basic propositions, the further than mind had the truth. Van Til's concept is that for relative human beings, they can have all needful truth but never perceive it as God does with his infinite knowledge of everything that affects any proposition. He charged Clark, therefore, with denying the incomprehensibility of God and Clark charged him with agnosticism since he that that for him it was impossible to know anything as God did. Clark wanted an absolute even if it were only in the single proposition.

This helped put into order some ideas that I've been mulling for a while:

Clark's argument is simple and effective: God is omniscient. What we know, then, must be what God knows. Self-defeating skepticism – to say nothing of questions such as what would constitute the real basis of union with Christ – is the alternative. Any proposition, which Clark defined as "the meaning of a declarative sentence" (Logic, pg. 28), is either true or false. Our mode and extent of knowledge may differ, but what man knows in comparison to what God knows is a separate issue from how [much] man knows in comparison to how [much] God knows.

That said, Rudolf's statement that "God knows every proposition in the context of all other propositions for Van Til" is extremely interesting, especially if taken in conjunction with Van Til’s denial that “[God’s] knowledge and our knowledge coincide at any single point” (cf. pg. 5, col. 3 here).

It is ironic that Van Til charged Clark with rationalism when Van Til held to the logical conclusion of Hegelianism. The doctrine of internal relations essentially states that “everything has some relation, however distant, to everything else” (link). If this is doctrine is true, as I think it must be – I may write a post on this later – then the question is begged as to how one can learn anything. I have argued (here, for example) that internal relations means that the source of knowledge must be an eternally omniscient being.

However, I do not think, as it seems Van Til did, that a precondition for the content of man’s knowledge to be univocal with that of God’s is that he too must know all relations. The definition of a subject may be the sum of that which may be predicated of it – and thus all subjects will relate to each other, positively or negatively – but contrary to Hegel, propositions rather than subjects are truth-bearers. So that men cannot attain comprehensive knowledge of a subject – such would require knowledge of the way in which the subject relates to all other subjects which, in turn, would require omniscience – does not mean men cannot know anything at all about a subject.

The problem may be that Van Til conflated knowing what a proposition means with how a proposition is known. In Rudolf’s analysis, for man not to know in “the way God does” or “as God did” is a bit ambiguous. It is true man doesn’t know “the way God does” insofar as man’s knowledge is discursive rather than intuitive. But does Rudolf additionally mean that Van Til didn’t think men “know some of the same things that God knew,” obviously a reference to the univocal meaning of a proposition?

If so – if Van Til did not think that man’s knowledge was univocal with God’s knowledge (as The Text of a Complaint implies) because men learn truth, and only portions at that – then it should be made clear that “analogical” knowledge and its devastating consequences can be avoided by noting that God can univocally communicate His eternal thoughts to man by divine illumination pertaining to what He has revealed in His word. This is the method by which a man comes to univocally know both the truth of propositions and, hence, the infima species of the subjects of propositions by which one subject is individuated from another. The issue then simply becomes a comparison of the extent of our knowledge [about a subject] to God's, and no Clarkian thinks he is omniscient. We are sanctified by God's word - the word of truth, not a mere analogy thereof.

Still, knowledge of certain propositions requires a context, as Clark himself notes in Today’s Evangelism: Counterfeit or Genuine? For example:

Page 66: There are many who in that day will say to Christ, Lord, Lord. And he will profess, I never knew you. Thus, clearly, a verbal profession of Lord is not saving faith. One must understand what the term Lord means. Further, as has already been pointed out, the name Jesus must be correctly apprehended. Confess that the Jesus of Strauss, Renan, or Schweitzer is Lord, and you will go to hell.

Page 85: Even the intellectual work of coming to understand a sentence requires assent and volition. It does not require assent to the truth of the sentence in question; but it requires a voluntary act of attention, and assent to the truth of other propositions by which its meaning is uncovered.

So I think Rudolf sells Clark short here. It is true that assent to the isolated statement “Jesus is Lord” does not necessarily mean that one knows its biblical meaning; he may be assenting to a falsehood. But the point is that one doesn't need to know the biblical meaning “in the context of all other propositions” in order to know what God knows. It is sufficient to know the infima species of the biblical subject “Jesus,” i.e. a minimal, finite number of propositions which would individuate “Jesus of Nazareth” from “Jesus of Strauss” et. al. Omniscience is not required. In fact, it shouldn’t come as a surprise that for a Scripturalist, the “context of propositions” in which the biblical meaning of the statement “Jesus is Lord” is properly understood is found in the very context of Scripture.