Clark's Gradual, Metaphysical Synthesis

A recent question was asked about Clark's theology proper which allowed me to collect thoughts that I have been meaning to put into words for some time. The question was as follows:

Clark was known to have translated John 1:1 so that the Logos was rendered as "Logic". Along these lines, Clark would argue to the effect that logic is the manner or characteristic of God's thinking.

How or where does Clark deal with the objection where logic is the art which orders discursive thought (something of which God does not have)? In other words, how can logic (as that which applies to reasoning from premises to conclusions) be said to be the characteristic of God's thinking if God's thinking is non-discursive?

This is an excellent question in that it draws out some implications of Clark’s view that may not be immediately obvious to the ordinary reader. 

Several people who responded to this question pointed out that an answer to it might depend on what the questioners thinks characterizes “discursive” reasoning. Clark himself used the word "discursive" to mean different things in different contexts.

For example, does “discursive” reasoning in the context of the above question involve a temporal succession and/or dependent process? If so, Clark would reply that God’s knowledge is not "discursive" in this sense:

The Complaint admits that Dr. Clark distinguishes between what may be called the divine psychology and human psychology in the act of knowing. God’s mode of knowing is intuitive, while man’s is always temporal and discursive. This distinction, the Complaint claims, is insufficient; a further distinction is needed. It is obvious therefore that the complainants hold to a two-fold theory of something in addition to a two-fold theory of the act of knowing. (Winter 1946/1947. Studies in the Doctrines of the Complaint. PCA Archives and SDCS)

Or does "discursive" merely suggest (in the context of the above question) that one’s thinking is syllogistically ordered? If so, Clark would reject the questioner's premise that God’s thinking is not "discursive":

God's knowledge is sometimes called intuitive rather than discursive. These terms are unfortunate, because if discursive means “syllogistic,” then God thinks in syllogism (Rom 4:2-3), and because men also presumably have intuitions. (1972. In Encyclopedia of Christianity. Philip E. Hughes, ed. Marshallton, Delaware: National Foundation for Christian Education. Feuerbach, Ludwig A.)

For Clark, however, for God to think "in syllogism" does not mean that there is some so-called fundamental truth or truths from which God must deduce all others. That would mean there would be more fundamental parts of God than others since, for Clark, God just is truth itself. I'll return to this point below, but by way of anticipation, I think Clark does implicitly provide answer to the questioner's confusion (although in such a way that it still leaves problems with Clark's larger theology). 

I'll put it another way: for humans, Clark says the law of contradiction is a test that requires supplementation – God’s word – in order for knowledge to be possible. For God, this is not so:

The substantive point needing discussion is whether the law of contradiction is the one and only test of truth.

Ideally or for God this seems to be the case. Since there is nothing independent of God, he does not conform truth to an alleged reality beyond truth and beyond him. Since there is no possibility of “vertical” (to use Carnell’s terminology) coherence, the “horizontal” test, or, better the horizontal characteristic of logical consistency seems the only possible one.

Weaver correctly notes that I do not claim for human beings the ability to apply this test universally. In this sense it is a “negative” or, better, an incomplete test. For this reason it must be supplemented some way or other...

Undoubtedly I hold that truth is a consistent system of propositions. Most people would be willing to admit that two truths cannot be contradictories; and I would like to add that the complex of all truths cannot be a mere aggregate of unrelated assertions. Since God is rational, I do not see how any item of his knowledge can be unrelated to the rest. Weaver makes no comment on this fundamental characteristic of divine truth.

Rather, he questions whether this characteristic is of practical value, and whether it must be supplemented in some way. It is most strange that Weaver here says, “I must agree with Carnell,” as if he had convicted me of disagreeing with Carnell by providing no supplementation whatever. Now, I may disagree with the last named gentleman on many points, but since it is abundantly clear that I “supplement” consistency by an appeal to the Scripture for the determination of particular truths, it is most strange that Weaver ignores my supplementation.// (Clark and His Critics, 2009, pgs. 287, 290)

A shorter statement by Clark to the same effect is as follows:

One who believes in the unity of truth may still believe that the false system entails contradictions; but to prove this is the work of omniscience. (Historiography: Secular and Religious, 1971, pg. 370)

Now, the following is very important: Clark held to a coherence or consistency theory of truth.

This gentleman distinguishes between logical consistency and a coherence view of truth. Since he stresses the latter rather than the former, he might think that Nash rates me too highly by asserting that I hold to coherence. However, neither Professor Nash nor I acknowledge this distinction, and while I now prefer the word consistency for clarity’s sake, I have no objection to Nash’s statement at this point. (Clark and His Critics, 2009, pg. 142)

For that reason, I believe, Clark came to reject that there could be multiple propositional systems that are completely coherent or consistent. If truth is coherence or consistency, there must be only one completely consistent or coherent system. Clark considered this even as early as 1952. From the Introduction to his A Christian View of Men and Things, he writes:

Now, there is a theory that the ultimate test of truth is coherence, and on this theory it would be impossible to have two self‑consistent, mutually contradictory philosophies. A false statement, so it is said, will always, if pursued far enough, imply its own falsity. If this coherence theory of truth should be established, then we could rely with confidence on this application of the law of contradiction. Its sufficiency would be inherent in the nature of truth. The mere fact that the coherence theory of truth would eliminate a final impasse might even be reason enough for adopting it. One might hold that all other theories of truth lead to skepticism, and that therefore the coherence theory alone is coherent and true. Possibly all this is so, but surely it needs some more talking about. And in talking about it, there can be no logical objection to using the law of contradiction as far as it will go.

Over time, I think his acceptance of a coherence theory of truth pushed him to accept necessitarianism (see here). There is necessarily only one coherent or consistent system of propositions, and God necessarily just is this system.

For Clark, the idea of multiple propositional systems that are coherent or consistent would not only have posed an epistemic difficulty for God but also a metaphysical one since, for Clark, God just is truth. Clark himself says: "Truth is God... God is truth." (1984. In the Beginning. The Trinity Review Nov.-Dec.). This dovetails with his theory of personhood in which persons just are that which they think:

As there is no temporal priority, so also there is no logical or analytical priority. Not only was Logic the beginning, but Logic was God. If this unusual translation of John’s Prologue still disturbs someone, he might yet allow that God is his thinking. God is not a passive or potential substratum; he is actuality or activity. (1980. God and Logic. The Trinity Review Nov.-Dec.)

God thinks truth; therefore, God is truth. Returning to an earlier point, for Clark, the unity of truth (God) is such that any single, true proposition will mutually entail all others, whereas a false proposition will always lead to systematic inconsistency. God has no need for axiomatic truths (unlike us), for He is in no need of "supplementation" (unlike us) to apply the law of contradiction to Himself - or, what is equivalent, to His own knowledge - with complete sufficiency. God just is the singly coherent, consistent, necessary, logical system: truth itself. God is this truth actually and actively. There is no potential for God to have been another system of so-called truths. 

Roughly, then, one can argue that epistemological beliefs Clark became committed to in the 1940s-50s - e.g. man's knowledge is univocal with God's; coherence theory of truth; anti-empirical means of knowledge - shaped his later, metaphysical views. For example:

- Clark's theory of truth was such that in order for Clark to account for knowledge of persons (e.g. man's knowledge of God or God's knowledge of men), he believed he had to change his views (cf. his earlier anthropological views here) by collapsing personhood into 1) propositions or 2) thoughts. 

[As an aside, these two positions might be distinct (link). In particular, the second position - i.e. persons are what they think - might seem to require what Clark calls elsewhere a "subjective, psychological act" (link), implying something seemingly distinct from propositional objects yet corresponding to them: i.e. thinkers. 

An interesting question is whether Clark believed these positions were distinct. It does not appear so, for in his book The Trinity, he says in the same chapter ("Individuation") that persons are a "collection of thoughts" and that his wife is "merely a set of propositions." He appears to equate positions 1) and 2), at least in terms of his own, proposed definition of personhood.

So did Clark think propositions can think themselves? Is this intelligible? And contrary to contemporary philosophers, did Clark think propositions have causal powers? Combined with his quote from the "God and Logic" article above, it does indeed appear Clark thought such to be the case! Of course, an obvious, unfortunate product of this position as held by elder Clark is a two-person theory of the incarnation (two thinkers = two persons).

On the other hand, even if our "subjective, psychological act" of believing might itself be a proposition, Clark does nevertheless seem to introduce something distinct from propositions elsewhere in accepting Clark's acceptance of a "Platonic-Philonic" dualism (link). But this then begs the question as to whether one must know phenomena qua phenomena or if it suffices to know the noumenal, suprasensible world. Likewise, Clark's theory of language trades on nonpropositional "symbols" which, in Clark's own words, correspond to propositions (link). 

This would be problematic unless the following assertion Clark made to Buswell in 1948 is false: "The correspondence theory would require us to compare an idea we have in consciousness with some utterly unknown object." But if it is false (as I've argued, link), it demotivates Clark's reason for accepting the coherence theory of truth and, in turn, the many metaphysical views Clark was led to as a result.]

- Likewise, Clark's theory of time as a "succession of ideas" suggests yet another collapse of a metaphysical category into an epistemic one. 

[Another aside: I wonder if this may function to explain why Clark waffled on the age of the earth prior to the creation of man. Clark did believe angels had successions of ideas; I suppose only the hypothesis that angels were the first creations would prevent one from asking Clark "how much time elapsed between the creation of the heavens and the creation of angels?" This question might be problematic if no angels existed to have a succession of ideas according to which the elapse between the creation of heaven and the creation of angels might be measured.]

- Returning to Clark's metaphysic of persons, one might suggest that whereas Thomistic divine simplicity is subject to comparison to Plotinus' One, Clark's version of divine simplicity is more subject to comparison to Plotinus' Divine Mind (link). To the chagrin of adherents to these versions of divine simplicity, I think the comparisons are warranted.

To expand on Clark's view, it is fairly apparent that Clark's affirmation of univocal knowledge plays a part in his unique understanding of divine simplicity. If Clark can be categorized as a classical theist - for he did accept divine simplicity, immutability, timelessness, and impassibility - he is certainly an odd one! On the other hand, that a comparison to Plotinus might nevertheless be made to Clark's views might lead one to theorize that Clark had a tendency to overly depend on ancient philosophers (with whom Clark was so familiar).

- In support of this thesis, 1) Clark's view of time depended on Augustine; 2) elder Clark seemed to deny the possibility of an infinitude of knowledge in The Incarnation, a denial which Steve Hays once point out presupposes a pre-Cantorian definition of "infinity" and simultaneously demonstrated Clark's ignorance of mathematics (cf. Personal Recollections, pg. 117); 3) elder Clark's acceptance of necessitarianism is somewhat similar to Plotinian necessitarianism. In this last case, however, I would say his view is rather more similar to that of Leibniz, which is nevertheless striking in that so far as I am aware, elder Clark never responded to his own, proleptic criticism (written in 1957) of his later acceptance of necessitarianism: 

If all truths are to be deduced by logic alone from the being of God, this world cannot be the best of all possible worlds because there are no other possible worlds. Are the theorems of geometry the best of all possible theorems? The question is meaningless, for there are no other theorems. God, therefore, exercised no choice in causing the world; he is its cause in precisely the same sense in which the axioms of geometry are the cause of the theorems. (Thales to Dewey, pg. 327, 1957)

Clark wrote other criticisms of necessitarianism he also neglected to address when he later came to accept the position (cf. Karl Barth’s Theological Method, 1997, pg. 36).

- One final metaphysical category that seems driven by Clark's epistemic beliefs pertains to causation. I've suggested that elder Clark's acceptance of occasionalism (link) was due to his anti-empirical epistemology. Clark might have feared that an alternative account of causation would support his critics, who perpetually asked if Clark had to read his Bible in order to know its contents. 

Now, I've also argued there was no reason for Clark to have had this fear (if he did; link). It is possible for propositional truths to correspond to nonpropositions - and even for the truth-values of contingent propositions to be determined by nonproposition[s] (for God Himself is not a [set of] proposition[s], link) - without devastating a revelational epistemology. Additionally, in the context of the specific critique regarding the reading of one's Bible, it is possible Clark conflated the basing relation in epistemology (or something like it) with causation simpliciter.

These are the beginnings of an interesting story one might tell about how Clark's unique thought developed and converged over time, a story I eventually hope to narrate in a more ordered form. 

As a perhaps unnecessary outro, I don't agree with Clark on several of these points. Nor were his views on several points I've outlined above always the same. For example, as I point out in one of the above links and quotes, one will find statements earlier in his life in which he (correctly) rejects necessitarianism. 

However, I think there is a gradual, metaphysical synthesis in Clark's thought that implies his awareness of such problems as the one posed at the beginning of this post. Even though I think Clark gets quite a few things wrong, his attempted synthesis is nonetheless impressive. Clark's following speech "from the grave" was a little too humble: "Clark never had much to do with ta meta-ta-phusica."

Thoughts on Contemporary Epistemology

I recently received Contemporary Debates in Epistemology as a birthday present. I was curious was the hot topics are among the epistemologists of today and figured that sooner or later I should branch out my reading if I seriously intend to pursue a degree in philosophy. Anyway, there are eleven topics debated in this book. I won’t go through all of them, not the least reason for which is that I don’t feel I have an adequate grasp of all of them. But among these topics are closure, skepticism [with respect to the external world], contextualism, and infinitism. With so many opinions, it’s hard not to find someone to [dis]agree with. It’s a mixing and matching. You have to read critically, i.e. you can’t just cross someone off for making one point with which you disagree. I disagreed with Dretske regarding closure, yet I think he makes a good argument against contextualism. The same goes for my readers. I’m sure I made bad points. Hopefully, I made some good ones too, and I hope further these points are not overridden by my bad ones. Now then, with respect to this book, you’ll have to get it to read specifics one way or the other, as I’m just going to comment on a few points that were of interest to me:

Closure

Closure is the idea that “If S knows p and knows that p implies q, then S is in a position to know that q” (pg. 2). On the face of it, this seems obviously true. Another author, Richard Fumerton – whose helpful distinction between necessary and sufficient conditions for knowledge I have quoted on this blog before (link) and whose books Epistemology and Metaepistemology and Skepticism would seem to be worth a look – remarked in a footnote of an essay on a different subject that “the bottom line is that if a philosopher advances a view that forces us to reject closure, that should be taken as a reduction of that philosopher’s view” (pg. 96). A very well made and succinct point.

The reasons why one would reject closure, however, make it a worthwhile discussion. One reason to reject closure is that it allegedly makes possible “ordinary knowledge.” If we reject closure, we could in principle know, for example, that “John ate all the cookies” without having to know “There are physical objects,” “There are other minds,” or “The past is real” (pg. 3). “John ate all the cookies” may implies these propositions, but we don’t have to know these propositions to know “John ate all the cookies” if closure is rejected. Likewise, we wouldn’t have to worry so much about Descartes’ demon, solipsism, and recently spontaneously generated universes.

Of course, we could accept closure, these “heavyweight implications” of so-called ordinary knowledge, and on these accounts reject ordinary knowledge as infallibilistic. In fact, as a Scripturalist, that seems highly preferable. Much of what we say or do are not based on beliefs which can’t be mistaken. Clark was right to throw the objection that he couldn’t know his wife back in the faces of his critics. So what if our knowledge of such isn’t infallible? The more interesting question is what knowledge is infallible.

Skepticism

This brings me to the issue of skepticism with respect to the – or perhaps “an” would be less question-begging - external world. Surprisingly – pleasantly surprisingly – the two authors seemed to agree that “we cannot avoid knowledge skepticism with respect to the physical world if we understand knowledge as requiring justification so strong that it eliminates the possibility of error” (pg. 86). [This too was written by Richard Fumerton.] His reference to a sort of justification which would preclude the possibility of error is another allusion to infallibilism, which I wrote about here a few months ago. Scripturalists will do well, I think, to focus on metaepistemology – the definitions of knowledge, epistemic justification, truth, and the like. It may turn out there is more agreement to be had with the scholastic paragons of contemporary epistemology than one could hope for.

Contextualism

If I understand contextualism correctly, it rests either on an equivocation of the meaning of “knowledge” or is a flat contradiction, neither of which is particularly useful. It basically says (pg. 45):

…whether S knows something – that she has two hands, for instance – depends on the context of the person who is saying S knows it. If I, a philosopher, worried about brains in vats and Cartesian demons, say it, then S doesn’t know she has two hands… But if S, an ordinary person on the street, someone without the least tincture of philosophy, says she knows that she has two hands, what she says is true. She attributes knowledge to herself in an ordinary, practical, context, in which demons and handless-brains-in-vats are not relevant possibilities… 

So who, according to contextualism, is right? Am I, a philosopher, right when I (given my context) say that nobody knows they have hands. Or is S right? We are, I’m afraid, both right. And that is where my low opinion of contextualism comes from.

If there is an equivocation – if what S means by “knowing” she has two hands is different from what the philosopher means when he says S [does not] “know” she has two hands – then rather than preserving knowledge of having two hands, it just highlights that S is probably not squarely facing the skeptic’s challenges (cf. the “heavyweight implications” in the section on Closure above).

Infinitism

Of all the debates I skimmed, this and perhaps the debate on a priori knowledge seemed to arouse the most incredulity from any of the debaters. The ideas that infinitism could be true or that there is no a priori knowledge are, thankfully, seemingly minority positions. With respect to infinitism in particular, the closing paragraphs from the detractor will close out this post (pg. 155):

In my essay I said that the (to my mind) most severe difficulty with Klein’s infinitism is that it is committed to the thesis that inference alone can create justification. Here Klein seems to embrace this commitment wholeheartedly, holding that the longer the chain of inferential justification for a given belief the greater the justification created, and that, if the chain is long enough (but still finite), the justification can “increase to the degree required for knowledge.” This seems to give us the result that knowledge does not require infinitely long chains of inferential justification after all: infinitism gives way to inferentialism. Worse yet, given Klein’s thesis that inferential justification is the only sort of justification there can be, we seem to get the result that one could start with a belief (or set of beliefs) that is totally unjustified, because it lacks any inferential justification, and by spinning out a long enough chain of inference from it reach a belief that has the degree of justification required for knowledge. 

These results are so counterintuitive that I hesitate to attribute them to Klein. But how else are we to interpret the quoted remarks?

Fuzzy Language

From pgs. 205-206 of A Christian View of Men and Things:

Now, any given word must signify one thing, or a finite number of things, or an infinite number of things. If the word has a finite number of meanings, then it would be possible to invent a name for each meaning, so that all words would have a single meaning. But if each word has an infinite number of meanings, reasoning and conversation have become impossible, because not to have one meaning is to have no meaning. But if a word has a meaning, the object cannot be both man and not-man. If the skeptic attempt to avoid the arguments, he might do so by saying nothing. In this case, however, there is no skeptical theory awaiting refutation. Or he might accuse Aristotle of begging the question by using the law of contradiction. But, then, if he says this, he has said something, and has himself admitted the force of logic.

While true, I don’t think the above is meant to suggest fuzziness in language is entirely useless. In some cases, ambiguity seems preferable. In particular, I’m thinking about instances of justified deception. A Nazi shows up on my door asking if I am hiding Jews. I respond, “there are no Jews here.” Now, through no fault of my own, the Nazi might interpret this to mean I am not hiding any Jews “at all,” whereas I actually meant I am not hiding Jews “in the visible vicinity.” The fuzziness lies in the meaning of “here.” Obviously, I didn’t answer the question the Nazi asked, but then again, I am under no obligation to answer him in the first place.

Now, if there were no ambiguity in language, I obviously could not deceive a Nazi. At best, I could say “search for yourself.” But if he persisted in questioning me, he would come to realize I was intentionally avoiding his question. What would follow I would consider to be less than desirable. So there is good reason for language to be fuzzy, though in an ideal world – a world without Nazis – clarity would be a worthy goal.

Clark's Lectures 5

I was fortunate enough to go to New York this past weekend and obviously wanted to see the public library, but I had no idea I'd discover that they had a copy of Gordon Clark's thesis for his doctorate at UPenn. Unfortunately, it was only a fragment of it, as the rest of the pages seem either to have been torn or fallen out at some point - there were perhaps 20 of the original 50 pages. Nevertheless, what I read impressed on me how much Clark must have developed his personal philosophy over time, even though it was obvious that Clark then was an able philosopher, fluent in multiple languages and ancient philosophies. At any rate, it was a pleasant surprise to find it, and I hope others will enjoy these few points he made that I transcribed:

History, Textual Criticism, and Skepticism

The opening sentence to his thesis was as follows:

Page 5: "Save us, we pray, from those who have so entombed themselves in the dark and damp of antiquity that they no longer appreciate the light of the present day; but save us all the more from those who go blithefully on their way in utter disregard of the lessons the past can teach."

The point of his poetic remark is well-taken but, if taken strictly, is stated a little imprecisely. The past doesn't teach. Its utility lies in its capacity to occasion ideas in our minds as to what is truth. I think I have addressed this issue here, but perhaps a further comment on a statement by Clark will be helpful:

Page 10: "In the case of Aristotle we are not dependent on fragments, for we have his complete works; we are perfectly familiar with the usages of his language; the only difficulty is textual and whoever bases a skepticism in textual criticism asserts that not only nearly all philosophy, but nearly all history as well, before the Renaissance, it forever unknowable. This is a reductio ad absurdem. We can with tolerable certainty ascertain the exact working of Aristotle, but to understand his thought we need also to know the arguments and discussion of previous arguments men which were the motives to his solution. Are these unknowable? My answer would be, try and see."

I thought it was ironic that Clark should have logically followed the implications of textual criticism so closely only to derive a conclusion opposite to what should be drawn from his philosophy of Scripturalism, viz. it is indeed the case that nearly all history is unknowable, since textual criticism often presupposes an empirical methodology. This is not a reductio ad absurdem to the individual who believes that man is efficiently illumined by God, though not necessarily apart from experiential stimulation. Of course, it would be silly of me to heavily criticize a man's early writings when it is that man whose theology I consider myself occasioned to be so indebted.

The Thesis

The purpose of his thesis, Empedocles and Anaxagoras in Aristotle's De Anime, was to determine how trustworthy Aristotle was in his historical interpretation of the philosophies of his forebears', with particular attention to Aristotle's treatment of Empedocles and Anaxagoras. He was well aware that his conclusions were tentative due to the focused nature of his thesis, but he believed that similar studies would solidify his generalizations:

Page 6: "What would be necessary for the final verdict on Aristotle would be a series of such theses, treating each philosopher referred to in each of Aristotle's works. Only after such an induction could generalizations be made. But how easy it is to anticipate the generalizations without going through the induction is perhaps only too well illustrated in the following pages."

Page 7: "The firm belief in the final truth of his own system led him to examine others through Aristotelian spectacles."

Page 46: "It appears, therefore, even in the little so far covered that A. is as trustworthy as any historian can be expected to be."

It is too bad that the majority of the pages between these last two statements were missing, as it is otherwise difficult to reconcile them. Perhaps he meant that although a historian cannot be trusted as an objective, unbiased source of information, he can be relatively charitable. But at least this shows Clark seemed to recognized a distinction between incomplete and complete induction and that his work falls under the former category.

Theological Statements

As much of Clark's thesis concerned itself with finding out what Empedocles, Anaxagoras, and Aristotle taught, there is less of the author's own opinion than may be desired. But this is proper, and it leaves me with only a few more interesting statements:

Page 45: "Now obviously to argue from a man's theism what his psychology ought to be is rather precarious."

I do not believe Clark would have considered this idea to be so obvious later in his life. But again, Clark was only 26 or 27 when he wrote this, so it is not strange that over the next 55+ years of his life that he would change his mind on a few of his beliefs. He apparently changed his mind on the infinitude of God as well (cf. The Incarnation, pg. 62):

Page 46: "The knowledge of an infinite mind, which is not the result of a learning process peculiar to finite minds, may be compatible with impassibility. Yet the more we insist that God is unchangeable, the less we understand how he recognizes temporal events as having happened or as about to happen."

This last statement is profoundly true, reflecting my current struggle to understand God's immutability in relation to time. As Clark changed his mind, I may very well change mine. But it is good to share a God whose truthworthiness is unchangeable.

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).