Some religious groups are pushing the teaching of “divine mathematics”: elementary-level mathematics education with a religious slant. This news has been making the rounds on liberal political websites, with the expected combination of horror and mockery. But I don’t think there is anything wrong with including God in mathematics education… as long as it’s done properly.
I first heard about this topic on the David Pakman show, and have since seen it discussed on other websites as well. The general idea of the movement is that some schools are hoping to teach Elementary school students that mathematical equations and laws are not “arbitrary rules” but in fact reflect a divine purpose or plan. An excerpt from a textbook that espouses this perspective is this:
The elementary student does not need to “understand” 2 + 2 = 4 in order to learn it and use it; he will learn the abstract principles later. But the elementary student does need to see his multiplication tables as part of the truth and order that God has built into reality. From the Christian perspective, 2 + 2 = 4 takes on cosmic significance, as does every fact of mathematics, however particular.
On the David Pakman show, they discussed that fact that this mindset could be used to undermine critical thinking. They said that it could be used to indoctrinate people from an early age to “just accept” things instead of thinking them through. They mention that it could be used as a way of shoring up opposition to the inclusion of God in other areas of education, like science. The logic is obvious: if non-creationists object to the teaching on creationism on the grounds that it would make the teaching of science unlike the teaching of other things like math, then obviously the next step is… change the way that you teach math!
All of these fears about the way that “Divine Mathematics” might affect critical thinking and the teaching of other subjects sound very plausible… but they are only speculation. If you take (for example) the quotation above, from the textbook, at face value, there is nothing about it that inherently is an argument against critical thinking. There is nothing about it that is inherently anti-scientific, or against the principles or spirit of mathematics.
Why not?
One could easily teach mathematics (or science, for that matter) from this perspective: God has created a wonderful and complex universe. Part of our mission as humans on this earth is to discover the rules and patterns and regularities that God has made manifest in this design. The process of science is the process of discovering, through reason and experiment and observation, exactly what structure God has imbued our universe with.
This was the mind-set of “natural philosophy” in the Middle Ages. Nobody questioned that God was behind everything that happened in the universe. Of course He is! The question of the natural philosopher was: what are the details?
Of course God made the apple fall from the tree! But what mechanism did He use? We will call it gravity, and then we will study the nature of gravity. We will ask: what are the properties that God desired gravity to have?
Of course God has created all of the colors in our beautiful world! But what is the mechanism that He created that allows us to see them? Study the eyes, study glass and prisms and starlight.
Discovering how white light can be broken down into the rainbow or why different colors of light have different properties wasn’t viewed as contradictory with belief in God. Quite the opposite: they were part of a very spiritual quest to answer the question: “what is the manner in which God has commanded the universe to work?”
Everything from Superstring theory to the details of non-Euclidean algebra can be viewed this way. They are exacting and analytical ways of asking, “What is the nature of this amazing and complex thing that God has created?”
Moreover: there’s nothing wrong with that.
There is nothing about that perspective that inherently limits or cuts off any scientific investigation. If a child is taught that Euclid’s theorem reflects a Divine Plan, it doesn’t mean that the child no longer has to learn the proof of Euclid’s theorem… because learning that proof is a deeper form of enlightenment: it’s learning more of the amazing details of the Divine plan. And if, some day, that child discovers non-Euclidean geometry, there’s no weird conflict in the child’s brain about God being wrong, because non-Euclidean geometry is also part of the Divine plan. And that can lead to the student wanting to learn even more proofs about the nature of that other (Divinely-caused) geometry.
As long as the “Divine plan” is taught with that perspective, there is literally no “harm” to it at all.
The inclusion of “God” isn’t the problem.
Where is the problem?
The problem–as always–is with egotistical, power-hungry people.
The problem comes from human beings who claim to have direct knowledge of God’s divine plan, who claim that they cannot be questioned because they have this special knowledge, and that anyone who disagrees with them is a heretic and is to be marginalized. The problem is when fallible human beings claim that they know God’s plan and could not possibly be wrong and can never be questioned… that’s when it all falls apart.
That’s when it all falls apart, not only for science and mathematics, but also for institutional religion, by the way. But that’s a topic for another article.
My point here is that there is a right way and a wrong way to teach “divine mathematics,” if that is your inclination.
The right way is to say: “all mathematical laws come from God, and it is the job that we fallible humans have is to struggle to find out what they are! We are constantly coming up with and testing proofs and hypotheses to get a clearer view of those divine laws. Sometimes we are wrong, but we are striving to learn His plan.”
The wrong way is to say: “We who are writing this textbook have already discovered everything there is to know, and you should believe these divine laws that we write in this book because we know what they are and if you think we might be wrong then you are disagreeing with God and will go to hell.”
That’s the wrong way to teach Divine Mathematics, and that’s the way that liberals fear and make fun of. But I think it’s important to remember that it’s not the only way.
The fact of the matter is, there are actually some very interesting and deep philosophical issues that relate to mathematics. Why do geometric laws seem universal? Where do they come from? Are they properties that depend on some aspect of our physical world, or are they truly conceptually and logically invariant, belonging to some higher “cognitive” realm (as Plato thought)? These are great issues to think about, and I think that more students–not fewer–should be encouraged to think about them.
And if it leads them to think about God, then so be it… as long as they are still asking “why” and “how” and “could I be wrong?”
Greg, I really appreciate this comment: “Personally, I HATE the fact that we live in a society where there is such a strong and presumed relationship between believing in God and NOT being a critical thinker.”
As someone who left school at age 17 with no tertiary education, no interest in history, philosophy, theology and a minimal interest in science I have Christianity to thank for sharpening my interest and hopefully my ability to think critically. I have to admit I was a Christian for some 10 years before I had so much as heard of Christian aplogetics so it has been a long journey.
I think the biggest challenge to my ability to think through something in this early period was struggling with Martin Luther’s theology in his “Bondage of the Will” from then on I began to look more carefully at the Bible and now I try to be careful in evaluating any writing.
To quote Josiah above:”Critical thinking demands that we not sit back and accept the existence of God as axiomatic. ” couldn’t it be said with at least equal claim to intellectual honesty- “Critical thinking demands that we not sit back and accept the NON-existence of God as axiomatic. ”
What do you think of the presuppositional apologetic claim of Dr. Greg Bahnsen? found here:
[youtube http://www.youtube.com/watch?v=j1hSx2evTGM?feature=player_detailpage&w=640&h=360%5D
Transcript of it found here:
http://eyeonapologetics.com/blog/2010/12/09/transcript-the-great-debate-greg-bahnsen-vs-gordon-stein/
I don’t think we’re in disagreement on this. Recall I said “God exists” may not be verifiable or falsifiable, but given a concrete definition of God we can attempt to assess the truth value of this particular claim like any other, meaning we can still first and foremost think about these things in a scientific way as a means of trying to answer the question, and if it is determined the results are inconclusive—as I believe the claim “God exists” ultimately is in a strict scientific sense—then we are left with our philosophical musings in light of this very fact, which will serve as a premise for forming our conclusion about the existence of God.
I don’t take the strong atheistic position—“God does not exist”—because I believe the strong atheist runs into the same problem as anyone stating the proposition “God exists.” However, I deny “agnosticism” as a legitimate philosophical position on the matter. After the arguments for and against the existence of God have been made, we are still left with the question “Do you believe in God?” No, I answer, and that makes me an atheist. It is worth noting I may lightly throw around the claim “God does not exist,” but I do so only in the sense I would assert the toothfairy does not exist or that Russell’s teapot does not exist, but I digress.
Most importantly, you’ve perfectly made the case against teaching Divine Mathematics for me:
“The important feature of these propositions–and the reason that one’s belief in such things literally doesn’t matter to science–is that they do not INTERACT WITH beliefs that do actually participate in scientific theory … so whether you believe it or not has no impact. It literally, from a theoretical point of view, doesn’t matter…
“…When you say that, ‘God has willed to rules of Geometry to be what they are, let’s use mathematical principles to find out what those rules are’ … there is no impact of having that belief, one way or the other. There is no PREDICTION that comes from the belief, and there is no way to verify or disprove the belief. So, it’s not a SCIENTIFIC claim. You can believe it, or not…. it literally makes no difference to the mechanism of science.” (I wasn’t exactly sure how to work your blockquote tag on this.)
If belief in the existence of God is irrelevant to mathematics and science, as we both seem to agree, then we are almost compelled once again to ask my original question: Why teach Divine Mathematics at all? Why not teach just mathematics or just science? Why muddy the waters by postulating such things and pretending they have mathematical and scientific significance? It is not that I wish to shut theists out of the philosophical debate on the existence of God—on the contrary: I welcome them—but there is a time and place for such things. In the elementary or high school mathematics or science class is not the place for such assertions, unless the existence of God can be proven and furthermore proven to have some relevance or relation to mathematics and science.
“Why not teach just mathematics or just science? Why muddy the waters by postulating such things and pretending they have mathematical and scientific significance? It is not that I wish to shut theists out of the philosophical debate on the existence of God—on the contrary: I welcome them—but there is a time and place for such things. In the elementary or high school mathematics or science class is not the place for such assertions, unless the existence of God can be proven and furthermore proven to have some relevance or relation to mathematics and science.”
I can see that argument. But that’s still not an argument that it’s harmful. It’s just not an argument that it’s helpful. I guess that summarizes my feelings about it: I don’t think that teaching divine mathematics is intrinsically valuable, but I don’t think it is intrinsically harmful. On the scale from -5 to +5, I think it is a dead zero … as long as it is done (as I said in the original article) correctly.
When I was teaching Introduction to Cognitive Science, I spent a class on evolutionary psychology and the neurological underpinnings of motivation and emotion. It’s non-standard for a cognitive science class, but I’ve always been firmly of the belief that it SHOULD be included. So, I scheduled it to be the class before spring break (biggest cut day) and made it sort of an “extra” topic, for fun.
When talking about evolutionary psychology, of course you end up talking about evolution. So I had to spend a hot minute explaining that the proposition “organisms evolve” is not actually in contradiction to anything that any religion claims, and that you can in fact believe (if you want) that God created humans from scratch AND simultaneously believe that the structure of human beings also evolved over time since that moment of creation.
But this is how I phrased it, exactly, to the class: You can believe God created people, or you can not believe God created people. You can believe anything you want to believe, having to do with the existence or non-existence of God, and none of it has any impact on the types of evolution that we are talking about in class today.
That’s kind of how I think I would teach mathematics, too, IF the students (or teachers, or administrators, or parents, or whoever) brought it up. I would tell them: if you want to believe that God created the rules of geometry, that’s fine! If you don’t want to believe it, that’s fine too! It really makes no difference either way: either way, our job as humans is TO DISCOVER THE RULES OF GEOMETRY.
And you know what? Even as I type this, I find the idea of making that explicit to elementary school students weirdly appealing. After all, isn’t that truly the more liberal approach? Isn’t that truly the more free-thinking approach? Tell the students: HEY! You have these options.
Personally, I’d love to be able to push our culture in a direction where we untangled this largely circumstantial connection between “religion” and “not thinking/not analyzing”. I’d like to try to get our culture to the point where we more explicitly acknowledged that there is a way to embrace religion AND critical thinking, IF that is what you have an inclination to do.
Logic—all statements have a truth value: 1 if the statement is true; 0 if the statement is false. Now, some statements may not be verifiable, but that’s where validity, soundness, strength and cogency come into play. The scientific method provides us with a framework for assessing claims about the nature of reality. “God exists” may not be verifiable or falsifiable, but given a concrete definition of God we can attempt to assess the truth value of this particular claim like any other.
Well, I actually don’t agree that all (non-self-referential) statements (about the world) have a truth value. When it comes to ontology, I’m a radical constructivist. But I don’t know if that’s a garden-path that we want to pave at this particular time.
But even if you believe in the objective truth value of propositional statements about the world, you have already given an opening in this: “The scientific method provides us with a framework for assessing claims about the nature of reality.”
For assessing some claims. But not for assessing all claims. There are some questions that are speculative and that are, by their very nature, outside of the domain of science. What were things like before the Big Bang? Is observed “noise” in behavior data due to true randomness or just unaccounted for factors that we have not unraveled yet? What is going on right now in a planet that is 30 million lightyears away? And so on. There are tonnes of propositions that may be true or false, but that are not evaluable by scientific means.
There are some claims that lie outside of the purview of science, because they are intrinsically not tied to data or observables.
In these cases, you can take the “strong atheistic” position and say, “NO SUCH THINGS EXIST”. Or, you can take the “weak atheistic” or “agnostic” stance, and say: “Science provides no framework for assessing the answer to this question. It may be true, it may not, there is no way we can ever know, so I’m not going to waste my time asking the question.”
The important feature of these propositions–and the reason that one’s belief in such things literally doesn’t matter to science–is that they do not INTERACT WITH beliefs that do actually participate in scientific theory. There is no causal mechanism through which the existence (or not) of a planet that existed in a previous universe before the Big Bang could influence anything in our universe… so whether you believe it or not has no impact. It literally, from a theoretical point of view, doesn’t matter.
So when you say, “God causes hurricanes to punish sinners” you are talking about something that impacts measurable cause and effect, so there is where I have a problem with the invocation of “God”. It seems like this would be measurable: measure the amount of sin in cities that have been hit by hurricanes, measure the amount of sin in cites NOT hit by hurricanes, calculate an R^2, and so on.
But when you say that, “God has willed to rules of Geometry to be what they are, let’s use mathematical principles to find out what those rules are” … there is no impact of having that belief, one way or the other. There is no PREDICTION that comes from the belief, and there is no way to verify or disprove the belief. So, it’s not a SCIENTIFIC claim. You can believe it, or not…. it literally makes no difference to the mechanism of science.
Yes, I would like to talk about pragmatics for a moment: murder is happening, and it will not change no matter what you or I say or what legislation is passed. Therefore, we should not try to prevent murder, for doing so is impractical. Sound familiar? Now, I am far from equating the mere belief in God to murder, but rather using an extreme example to emphasize the point I’m trying to make. Just because something ‘is’ does not mean it ‘should be’, or that because something ‘is’ means it is desirable. I won’t debate the particulars of “is-ought” here, but I will say I do not believe this is the counterargument you wish to make on the point of pragmatism. It is, as you would say, “sloppy reasoning.”
I understand full well the relationship between science and faith many theists wish it to have, but I disagree with it. Belief in God may not be intended for participation in the scientific reasoning process, but that does not mean it is not susceptible to scientific reasoning all the same. All beliefs are in essence a claim about reality that is susceptible to scientific reasoning, whether professed aloud, kept to oneself or even consciously acknowledged. Granted some beliefs are neither verifiable or falsifiable, they can still be put to the test of scientific reasoning. Even simple, mundane beliefs that have little significance are susceptible to scientific reasoning, such as the belief that blondes are typically dumber than brunettes, men cheat on their spouses at a higher rate than women or homosexuals are more promiscuous than heterosexuals. The belief in God—the claim that God exists—is no different. It does not hold a privileged position because some people choose to wholeheartedly have faith in this belief. “Divine mathematics” is the mathematical equivalent of “intelligent design.” I still say no, and I don’t think this is because I have not stopped to question my own beliefs in my critical thinking.
“The belief in God—the claim that God exists—is no different. It does not hold a privileged position…”
Why do you believe that?
Why is it necessary to invoke the theory of God to explain the axioms of mathematics? What explanatory and predictive powers do we gain from accepting this theory? Furthermore, what evidence have we that lends support to such a theory? Critical thinking demands that we not sit back and accept the existence of God as axiomatic. By just accepting the existence of God as axiomatic, and that God has decreed both the physical and metaphysical, yes, we have suspended critical thinking on the subject in question. To quote Richard Feynman, “God was invented to explain mystery. God is always invented to explain those things that you do not understand.” But the truth is God doesn’t explain anything.
There may not lie any inconsistencies in claiming God is the be all and end all behind the universe and the metaphysical, and thus one can theoretically teach divine mathematics while remaining logically consistent, however it seems to me where critical thinking is affected (or at least temporarily suspended) is in accepting God as the primum movens. You mentioned that mathematics presents some very deep and interesting philosophical issues of its own, such as why geometric laws seem universal, where they come from and if they are properties that depend on some aspect of our physical world or if they are similar to Plato’s forms. It seems divine mathematics is content with God as the answer, and what I am arguing is that such an answer does nothing to resolve these very deep and interesting philosophical issues surrounding mathematics. So, again I ask, wherefore invoke the theory of God? It seems to me the place to begin is by questioning the axioms of mathematics themselves rather than complicating things by trying to factor in a non-quantifiable variable such as God. (There’s an entire branch of philosophy devoted to mathematics actually, as you’re no doubt aware of.) I don’t see how education or critical thinking is served by treating as fact someone’s supernatural theory of the universe. Critical thinkers who do believe in God would see this, I think, and I have no vendetta against people who believe in God, but as I said I’m skeptical of anyone who wants to implement divine mathematics into education. This is not solely a theoretical argument. There are practical arguments to be considered. Theoretically, I do not believe we are in disagreement. For practical reasons, though, I don’t think divine mathematics should be something taught in school. You’re saying teach divine mathematics, but do it right. I’m saying don’t teach divine mathematics—just teach mathematics. Divinity isn’t necessary.
Of course, if you REALLY want to talk about this on a practical level, then there is something you should know: In countless schools across the country, God already IS being taught as part of mathematics, just as God is already included in every aspect of school life. This is the way it is in countless small and medium-sized towns throughout the rural and even suburban deep south, and even to a degree in the midwest. If you want to talk about pragmatics: the inclusion of God is happening, and it will not change no matter what you or I say or what legislation is passed.
So the pragmatic question then becomes, which is the easier and more practical goal? To get these people to stop mentioning God in a school where the Christian Student Group is the biggest organization in the school? Or, to get them to teach that you can simultaneously believe that God created mathematics AND that we can question and learn and doubt theorems that have not yet been proven? That’s the only practical question — not whether it’s “necessary” or not.
But when you say this,
“What explanatory and predictive powers do we gain from accepting [God]?”
You are also misunderstanding the relationship between science and faith …. or at least, what I understand the relationship to be.
The acceptance of God, and of mathematics being part of God’s plan, is not a scientific hypothesis. Its function is not to have explanatory power. That’s why it’s faith.
Ideally (at least, in my opinion), it is completely sequestered from scientific thinking. It has no explanatory power, it plays no role in confirming hypotheses or proving theorems. It is a separate, specifically NON-scientific assertion. By saying “what role does it play in scientific reasoning?” you are making the fundamental error of thinking that it SHOULD, and of thinking that it is in the same class as scientific beliefs that partake in the scientific reasoning process. It is not. It is an article of faith that is separate and in addition to, that neither participates in NOT INTERFERES WITH (ideally), scientific belief and reasoning.
This is what I mean, when I talk about teaching it in a way that “does it right.” You can teach people to understand that belief in God can be kept separate from scientific reasoning: it does not have to erode critical thinking or be seen as interfering with scientific hypotheses. You can say : “Of course God created everything, but the task of science is to ask HOW it all works and in what MANNER these things have played out. To answer these questions, we use critical thinking and scientific method.”
There is nothing contradictory there. The only way it’s contradictory is if you mistakenly believe that the “belief in God” is INTENDED to participate in the scientific reasoning process. That belief, by the way, is very much a cultural construction. So in your critical thinking, you can try starting by questioning THAT belief… 😉
Sorry, but I’m on the side of the liberals fearing and making fun of this method of teaching. I suspect anyone adamant enough about using God to explain the laws of mathematics so as to officially include it in education (public or private) has an agenda. Let’s not be naïve here: It’s simply another way for religion to wedge its ugly foot in the door. You don’t need God to explain the laws of mathematics, because it doesn’t. As you adequately explained, the problem comes from human beings who claim to have direct knowledge of God’s divine plan, and I argue that anyone who claims to know that the laws of mathematics come from God are already claiming to have direct knowledge of God’s existence and his divine plan. That’s enough for everything else to get in the door. By this rationale, there are no objectionable grounds to stop people from claiming, say, that the laws of morality also come from God, and these seem to be a lot trickier to ascertain than the laws of mathematics or physics. People already do this, but to give them a free pass on saying the laws of mathematics are determined by God logically makes it acceptable to say the laws of morality are determined by God. The fact is by people claiming absolute knowledge of God’s existence and the certainty that the laws governing both the physical and the metaphysical are part of God’s divine plan, they may not be claiming to have discovered everything there is to know, but they are certainly claiming absolute knowledge of more than they’re capable of knowing, and this just shouldn’t be philosophically or scientifically acceptable. In sum, it’s a slippery slope. Yes, it does, in fact, undermine critical thinking, because accepting it implies the application of critical thinking is arbitrary. Therefore, I think the arguments against accepting this kind of hogwash are stronger than those for accepting it.
I just want to clarify the debate, and make sure that it comes into focus on the correct problem.
I’ve never been a fan of arguments-by-intermediaries. When a person says “I am against X because Y is bad and X could lead to Y,” for example. Or when someone says, “I am against X because the motivation Y is bad and I think some people might push for X because of motivation Y.” To me, it seems to place the blame in the wrong place: the blame should go on the actual thing that you consider undesirable (Y), not the thing that is correlated with or could possibly lead to the undesirable thing.
To me, it seems almost like a kind of sloppy kind of reasoning. I come across people who say, “I hate fat people.” I ask them: “Why?” They say, “Fat people are often lazy.” The fact is, there may be a correlation between being fat and being lazy, but what the person really “hates” isn’t fatness… it’s the presumed laziness. But the person is being sloppy, and taking the easy way it: “I can tell if someone is fat by looking at them, so I’m just going to criticize them for being fat.”
This seems analogous to what is going on here. What people object to is the attempt to undermine critical thinking. Putting God into the conversation doesn’t NECESSARILY undermine critical thinking…. but pointing out “God” and attacking the inclusion of “God” is an easy way out. It’s much less complicated than trying to identify, specifically, incidents where critical thinking is undermined.
But it’s putting the blame in the wrong place, in my opinion.
Personally, I HATE the fact that we live in a society where there is such a strong and presumed relationship between believing in God and NOT being a critical thinker.
I think it would be a service–to thinking people of all kinds–to drive the conversation out of that rut. I think it would benefit society immensely to have a stronger articulation of the position: there is a way to believe in God AND be a critical thinker, too.
By being wholesale against including God in the teaching of Mathematics, you are basically just going along with the rut—the presumption that God and “critical thinking” CANNOT co-exist.