Saturday, November 15, 2014

Nature's God and Math

All that has by nature with systematic method been arranged in the universe seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed like a preliminary sketch, by the domination of number pre-existent in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and eternal essence, so that with reference to it, as to an artistic plan, should be created all these things, time, motion, the heavens, the stars, all sorts of revolutions.

-- Nicomachus of Gerasa (60-120 AD) Source: God, Mathematics, and Intelligent Design in Antiquity

Did you know there is "No Such Thing as a Scientific Argument Against the Existence of God"? 

Sunday, November 02, 2014

Falsifiability and the Meaning of Genesis One

Thomas Pittman, PhD

San Jose, CA


This paper applies the scientific concept of falsifiability to propositions about the author's intent concerning Creation Week in the first chapter of Genesis. A simple but robust proof is given to show that it was the Biblical author's intent to teach a 144-hour duration for Creation Week, and that assertions to the contrary are either false or meaningless.

This paper was presented at the West Coast meeting of the Evangelical Theological Society in 1996.



Falsifiability is the essence of the Scientific Method. The working scientist proposes a hypothesis (a proposition or putative statement of fact concerning some aspect of his area of research), then devises one or more experiments designed to show the hypothesis to be false, if indeed it is false. Alternatively, the scientist may adopt some hypothesis already proposed by others in his field, but still devise experiments designed to show it to be false. The hypothesis that withstands this assault is promoted to the status of "theory" and eventually to "law of nature." However, to qualify as a working hypothesis, the proposition must be falsifiable, that is, it must be possible to devise experiments that in principle could show it to be false, even if in fact they fail to do so. A proposition that is not falsifiable is considered meaningless for scientific purposes; it may offer insight concerning some inner religious or psychological state of the speaker, but it says nothing about the real world that is the domain of science.

Consider the proposition, "The title of this paper contains no word five letters long." This statement is falsifiable, because we can devise experiments with at least one conceivable outcome that proves the statement false. One such experiment would be to examine the title of this paper, counting the letters in the first and last words. If either of these two words is five letters in length, the proposition has been falsified. That is a conceivable outcome, so the statement is falsifiable. However, when we perform the experiment and count the letters in these two words, we encounter lengths of 14 and 3. Neither of these is five, so the statement is not falsified by this experiment. However, it has also not been proved true, because there are other words in the title that were not examined by this experiment, and one of them could still be five letters long. Scientific experiments generally only establish a hypothesis as false, or fail to establish anything at all. Some other scientist could always come along with yet another experiment that succeeds in falsifying a hypothesis that has so far withstood all challenges.

Consider now the proposition, "Two plus two equals four." There is no experiment that can be devised with a conceivable outcome in which this is false. It is not falsifiable. We call a proposition that is necessarily true as this one is, a "tautology." Tautologies are valuable tools for studying mathematical and logical reasoning methods, but they tell us nothing about the real world.

Then there is the proposition, "Joe feels good." While this may be true or false at a particular point in time, no experiment can unequivocally prove it false. Try the experiment consisting of looking to see if Joe is smiling. If he is, perhaps it is because he heard a good joke; if not, does that prove Joe does not feel good? What if Joe is a Puritan, who may feel good inside but is not allowed to signal this feeling to the world by smiling? Statements about feelings are generally considered not falsifiable. From a scientific perspective they are meaningless.

We could continue to look at varieties of propositions to further explore the concept of falsifiability, but it would not greatly improve our understanding for the subject of this paper. Let me mention only historical statements, which may be true or false but the experiments to falsify them must often be inferential, because one cannot turn back the clock to better examine the attendant circumstances.

Linguistic Falsifiability

I now propose for your consideration, a variation on the issue of falsifiability, applied to propositions about a written text. The text most often considered among evangelicals is the Bible, and its great age poses special problems for falsifiability testing.

When I studied Greek, the instructor was an advanced student who rather cleverly (so I thought at the time) reasoned that learning all the noun and verb paradigms was unnecessary; it was sufficient only to learn to recognize the distinguishing characteristics of each form. I now consider that a mistake: the classical rote and drill method is better. The reason is falsifiability.

When you look at a Greek verb in context, one of the questions you might ask is, "Is the tense of this verb aorist or imperfect?" The imperfect tense would suggest repeated or continuing action, while the aorist would not carry that meaning. Thus the broader question, "Did the author intend to communicate continuing action in this sentence?" is falsifiable and meaningful, for it can be falsified by the "experiment" that determines the tense of the verb, when it turns out to be aorist and not imperfect. Similarly, the question about the verb tense ("Is this verb in the imperfect tense?") is falsifiable and meaningful, for it can be falsified by showing that its form is aorist. Of course to do that you must know what this verb would look like in the aorist tense, which is where the recognition method fails.

Let us look at a more specific example of the author's intent, in the following two sentences:

1. On July 20, 1969, Yuri Gagarin became the first man to set foot on the moon.
2. Hey diddle diddle, the cat and the fiddle, the cow jumped over the moon.

Both sentences are patently false, but we are not so much concerned with that as with the author's intent in writing them. Neither author is available for questioning, so we can only formulate hypotheses about that intent and devise "experiments" to test those hypotheses. Here are a some hypotheses to consider:

a) The author of sentence x intended to write poetry with no historical significance.
b) The author of sentence x intended to report a fact of history.
c) The author of sentence x intended to teach a theological dogma.

Each of these hypotheses is falsifiable, because like the tense of Greek verbs, we know the respective forms of poetry, historical facts, and theological dogma. To recognize poetry the analyst looks for rhyme and meter, and (often) the juxtaposition of words in ways that do not correspond to nature; sentence (2) is a good example of poetry. To identify modern historical facts the analyst looks for dates, places, and the names of real people; sentence (1) fits this description. Theological dogma typically involves God as subject or object, or else presents moral imperatives; neither of these sentences fits that description.

Applying hypothesis (b) to sentence (1) presents us with an interesting dilemma. Because the sentence is known to be false, is it possible that the author did not intend to offer a fact of history? The form of the sentence is clearly historical: you need only replace the name "Yuri Gagarin" with the name "Neil Armstrong" and it becomes a true fact of history. Here we rely on our external knowledge of history to corroborate or falsify the hypothesis about the author's intent. When that external knowledge is missing or in dispute it cannot be used in this way, and we must rely on the other factors.

It is also rare that one must evaluate the author's intent on an isolated sentence. Thus a single historical error could be discounted if sentence (1) were part of a larger historical treatise. On the other hand, if sentence (1) appeared as one of a collection of false statements, then the historical intent of the author might more readily be falsified.

Note that in each case we are discussing experiments to falsify hypothesis (b) as applied to sentence (1). No such experiments are even possible with hypothesis (d) below, which may perhaps be true or false, but there is no way we could verify or falsify it apart from asking the author:

d) The author of sentence x intended to record an encrypted password to his e-mail account.

Two Propositions about Genesis One

Now we are ready to consider some propositions about Scripture. In the first chapter of Genesis there is little question about the grammatical forms used or the lexical meaning of the words. Furthermore, it is placed in a larger context of historical narrative, and while it does exhibit some structure, it does not have the form of Hebrew poetry (of which we have many examples, some of them later in Genesis). I propose now to base my study of the topic at hand on this solid foundation, rather than on the shifting sands of scientific cosmogony. The first and most important question we can ask about these propositions is if they are falsifiable and therefore meaningful.

Propositions about the duration and recency of the Creation Week recorded in the first chapter of Genesis are historical in nature, and have been debated by scholars for centuries. The pair of mutually exclusive propositions, "The duration of the events reported in Genesis One did not exceed 144 hours" and "The events reported in Genesis One were spread over long periods of time," are both in principle falsifiable, and many scientists and theologians have expended much time and effort to devising experiments for the purpose of falsifying one or the other. I do not intend to add to that effort at this time. Rather let us consider a pair of second-order propositions, for which the evidence is simpler and less controversial.

Although these propositions refer to the inner thoughts of a writer no longer available for questioning, I think we can consider their falsifiability on the basis of external evidence. Indeed we have no alternative.

Let Proposition A be the statement,
 "The author of Genesis intended to teach no particular duration for Creation Week."

Let Proposition B be the statement,
 "The author of Genesis intended to teach a 144-hour duration for Creation Week."

Clearly, these are mutually exclusive: they cannot both be true in any meaningful sense. They are not collectively comprehensive because other propositions, mutually exclusive with both of them, exist. However, most of the participants in the debate concerning Creation implicitly defend one of these two only, and attack the other only.

Let us consider in turn the falsifiability of these two propositions. Any particular claim about an author's intent is most easily shown to be falsifiable by pointing to words or sentences which the author did not use, but if they had been used would have communicated the opposite meaning.

Proposition B is falsified by finding that the author used words communicating a very long duration for Creation Week. It is also falsified by finding that the author used words communicating no particular duration. The Hebrew language available to the author of Genesis contains words and constructs capable of both of these alternate meanings, and the author did not use either one. An example of words that convey no particular duration of time occurs in Genesis 4:3: "In the course of time Cain brought some of the fruits of the soil..." [NIV] Thus Proposition B is falsifiable but not falsified.

Proposition A is falsified by finding that the author used words communicating a specific duration for Creation Week, most particularly if that duration is 144 hours. The Hebrew language available to the author of Genesis contains no word for our modern concept of a 60-minute hour -- indeed nothing even closely approximating that concept shows up in the Bible until the time of Hezekiah (see 2 Kings 20:9-11). We can hardly burden the author of Genesis with terminology not in his vocabulary, so a transliteration of the English phrase "144 hours" is out of the question. However, we might expect the author of Genesis to enumerate atoms of the finest granularity of time available in his language to denote a specific time, as for example, "there was evening and there was morning, the sixth day." The author of Genesis, it would appear, did use an enumeration of that finest granularity.

Alternatively, we might expect a falsification of Proposition A to consist in putting the events of Creation Week into a one-to-one relationship with a period incontestably of a specific (and short) duration, such as the Sabbath week in the Law of Moses. As a mathematician by training, I note that one-to-one correspondence is exactly the modern mathematical proof for establishing a specific enumeration. It is unnecessary here for me to resurrect the debate over the meaning of day in Hebrew as it occurs in the first chapter of Genesis; it is sufficient to find exactly that one-to-one correspondence in the Ten Commandments: "For in six days the LORD made the heavens and the earth..." [Ex.20:11, NIV] Whether Moses was also the author of Genesis or not, his clear intent was to bind the Sabbath week to the six days of creation, and furthermore to specifically limit that to the standard 144 hours of the laboring man's week. Otherwise the man found gathering wood on the Sabbath day [Num.15:32-36] would have had a perfect defense for his life: "The Law, 'Six [indefinite] periods of time you shall labor' is for me ten years to a 'day' so I'm still working on my fourth day. When I am 60 years old, I will take a ten-year Sabbath rest." God and Moses did not see it that way.

Every possible wording for falsifying Proposition A that I can think of, within the vocabulary available to the author of Genesis, has already been used in the sacred text. Thus we are forced to conclude either that Proposition A is not falsifiable and therefore meaningless (except perhaps to give us some insight about the internal feelings of its proponents), or else it is falsifiable and false.


This leaves us with a rather robust conclusion: The author of Genesis did intend to teach a particular duration for Creation Week, and that duration is best described by the simple unambiguous modern phrase, "144 hours." Any denial of this conclusion is either illogical or inconsistent with the evidence.

It is important to recognize, however, that the force of the logic I have presented here says nothing at all about whether the duration of Creation Week was actually 144 hours, but only that the author of Genesis intended to say it was. We must fall back on other means -- specifically the principle of inerrancy -- to determine the actual duration of Creation Week. But I leave that debate to the scientists and theologians, in one or the other of whose domains it properly lies.


I prefer the phrase "144 hours" to "six days" because of the ambiguity introduced into the latter term by the so-called "day-age" theory. Once a term has been corrupted by verbal double-speak, it can no longer be used unambiguously in debate. Another example of this occurred in recent time when the new term "inerrant" became necessary to refer to what the traditional term "inspired" had formerly meant before it was corrupted by theologians opposed to the orthodox doctrine to which it referred.

About the Author

Thomas Pittman received his BA in mathematics at Berkeley, and his MS and PhD in Information Science at the University of California in Santa Cruz. He also spent two eclectic years at Trinity Evangelical Divinity School studying Greek, Hebrew, systematics, apologetics, etc. Apart from a 3-year position on the faculty of Kansas State University, he has spent most of his career developing custom and commercial computer software. He is currently Vice President of Magnify Software, a small software firm in San Jose.

(This paper was originally posted here.  It is re-posted here with permission.)