Tag Archives: Philosophy

Portraits of Christians – Leonhard Euler

Leonhard_Euler - portrait by Jakob Emanuel Handmann, 1753.
Leonhard_Euler – portrait by Jakob Emanuel Handmann, 1753.

In a time when our culture wants to denigrate Christians as stupid, backwards, anti-intellectual cretins opposed to science, I’d like to refresh our culture’s  memory with some portraits of some of the phenomenal, ground-breaking people who helped our science – and our society – advance. Not only did these people happen to be Christians, their beliefs were quite often foundational to their achievements.

The name Leonhard Euler (pronounced “oiler”) may not be a household name, but it is one familiar to many engineers. The Euler-Bernoulli Beam theory he developed with his friend Daniel Bernoulli became a cornerstone of structural engineering, and we still use the “Euler buckling stress” in column compression calculations 2 centuries after he died.  But his contributions to engineering were only a small part of his amazing résumé. Besides being considered one of the greatest mathematicians of all time and the top mathematician of the 1700’s, he also advanced the fields of physics, astronomy, and logic. If you’ve ever seen the symbol “e” (the base of the natural logarithm) on a calculator, you’ve seen one of 2 mathematical constants named after him (the only mathematician with that distinction). In math, he contributed to the fields of calculus, geometry, algebra, graph theory, and number theory. Science historian Carl Boyer compared the impact of his book on mathematical functions to Euclid’s Elements; Euclid’s being the foremost textbook of ancient times, and Euler’s the foremost of modern times. He won the Paris Academy’s Prize Problem (an international problem-solving competition of the 1700’s) 12 times. He extended Newton’s laws of particle motion to include rigid bodies. In logic, he came up with the graphical representation of a syllogism now known as an Euler diagram. Much of our math notation (such as the Greek letter Σ for summation) is due to him. If you’ve taken a math class anywhere between junior high and grad school, any general physics class, or any of several different engineering courses, you’ve been helped by (or, depending on your perspective, been tortured by) Euler’s analytical brilliance. Although the term isn’t used much anymore, Euler was a true “polymath” – one with expertise in a wide variety of subjects.

His credentials as a genius are unquestionable. And yet, he was also a devout Christian. He pushed the boundaries of math and science, and yet never felt that science had led him away from God.  In fact, he wrote an impassioned “Defense of the Revelation Against the Objections of Freethinkers”, a treatise against the atheists of his day. This is a roughly 14 page work laid out in 53 paragraph-length points to build a case that true happiness is only achieved through knowing and obeying God, and that the Bible is God’s gift to us to show us how to achieve that. He postulates that the human soul is exemplified by the exercise of understanding and will; that happiness consists in the “perfection”, or betterment, of a situation; that for humans,  the complete happiness of their soul depends on perfecting these two faculties of the soul – understanding and will. With regard to the first, Euler proposes, “The perfection of understanding consists of the knowledge of truth, from which is simultaneously born the knowledge of good.  The principal aim of this knowledge is God and His works, since all other truths to which reflection can lead mankind end with the Supreme Being and His works.” Regarding the second, he says that “the will of man should submit to the will of God in all respects and with the greatest exactitude.  Since God is the source of all good, it is obvious that the man who wishes to bend his will in this way must necessarily be in the happiest state.”[1] He goes on to (briefly) answer a wide range of objections to why the Bible is God’s road map to lead us to Himself.

After being asked to tutor Frederick the Great’s niece, he wrote 200 letters to her explaining physics and philosophy, but also delving into his Christian knowledge as foundational premises to his understanding of the world. Note, these are not compartmentalized statements of personal faith separate from his science and philosophy lessons. For instance, in explaining about the marvels of the eye to her, which was only then just beginning to be studied in detail, he wrote, “Though we are very far short of a perfect knowledge of the subject, the little we do know of it is more than sufficient to convince us of the power and wisdom of the Creator. We discover in the structure of the eye perfections which the most exalted genius could never have imagined.”[2] This coming from a genuine genius! Ironically, two centuries after Euler recognized it, we are still learning more about the complexity and amazing design demonstrated in the human eye (see my previous post on that topic here). I could go on with several other examples of the faith of this intellectual giant, but I’ll stop here and just say that Euler was one of many great scientists through the centuries who delighted in the study of God’s creation, and clearly recognized it as such. Do you?

[1]Leonhard Euler, “Defense of the Revelation Against the Objections of Freethinkers”, c.1740’s.
[2] Leonhard Euler, Letters to a German Princess on Diverse Subjects of Natural Philosophy, “Letter XLI”, written 1768-1772.

Get the Ump! (The Axiological Argument)

AP Photo by Butch Dill
AP Photo by Butch Dill

We’ve looked at several lines of reasoning justifying a warranted belief in God this last month. Today, we turn to what can be called the Moral Argument, or the Axiological Argument (axia = “value” in Greek).

Here is a common formulation of the argument[1]:
Premise 1: If God does not exist, objective moral values and duties do not exist.
Premise 2: Objective moral values and duties do exist.
Conclusion: Therefore, God exists.

That first premise may seem like a big jump, so let’s dig into that  deeper by first defining our terms clearly.

  • “Values” are the moral worth of something; its goodness or badness. For example, helping the sick or the poor is generally recognized as “good”, while murdering them is generally recognized as “bad”.[2]
  • “Duties” are moral obligations or prohibitions; the rightness or wrongness of something. Something may be morally good without being an obligation. Moving to India to care for lepers may be a morally good action, but it’s not an obligation anyone has to do.
  • “Objective” means independent of opinion or perception of the subject, and is intrinsic to the object discussed. It’s the same for all subjects observing that object. Contrast this with subjective, which is based on a subject’s opinion or perception of an object and can vary between different subjects.
  • “Moral” refers to standards of right conduct.[3]

And therein lies the rub; standards are enforceable, while opinions aren’t. Morality is defined as a standard, but standards come from independent authorities. When two teams think the other one cheated, what do they do? They call for a decision from the umpire, the referee, the judge – whatever that sport calls their independent rule-enforcer. But the umpire has to be independent of either team, and he can’t make up the rules as he goes. He applies a defined standard impartially (we hope). What if each of the 2 teams comprised half the world? Who would be left to be an independent judge? The Axiological Argument highlights this need for a “third party”to define the standards we as humans abide by. Now, to clarify, this premise does not say that those who don’t believe in God can’t live ethical lives, understanding moral duties and making morally good decisions each day. Premise 1 is an ontological statement – a statement of existence; namely, that if God doesn’t exist, there would be no objective moral standards for us (atheist or theist) to recognize and live by. They would not exist without God, because He is the only one in the position to be truly independent and objective. Anything we come up with is just one person’s idea versus another’s.

Are there any reasons to accept premise 2’s claim that objective values and duties really do exist? J. Budziszewski has noted that “There is no land where murder is virtue and gratitude vice.”[4] Even in Nazi Germany, the Nazis dehumanized their victims (so it wasn’t murder) in an attempt to justify what they did. While extenuating circumstances can seem to relativize morality, the “fun test” confirms morality’s objectivity. “What’s that?”, you say? It’s a simple way to eliminate the effect of extenuating circumstances in justifying decisions. To see if circumstances would change the moral value of something, add “for fun” to the end of it. Lying to protect Jews from Nazis may be morally better than being an accomplice to their murder, but lying “for fun” is never considered morally good. Murdering Hitler to save millions may be justified, but murdering even Hitler “for fun” is not. Justifiable circumstances can be found for other deeds like stealing, arson, lying, etc, where the bad deed is the lesser of two evils. In dilemmas where the only options are all bad, a person may be justified in choosing the “least worst” choice. But murdering for fun, stealing for fun, etc, are never condoned or viewed as “good”. In an extreme example, the unacceptability of torturing innocent babies “for fun” would reveal that we really do consider there to be objective standards that shouldn’t be violated in any situation.

Therefore, God exists. Too simple? True premises and valid logic leave no other alternative but a true conclusion. We have defined our terms to avoid ambiguity and have provided support for the premises, and the syllogism that makes up this argument is logically valid (i.e. no logical fallacies present).  What characteristics about God can be inferred from this? First, His nature is intrinsic perfect goodness that is the standard for moral values. Second, His will establishes the standard for moral duties. What are some consequences of this conclusion? Simply this: we are accountable for our actions, but thankfully, it is a level playing field and we can know the game rules if we choose to learn them. We have an infallible Umpire who, unlike humans, will never make a bad call.

[1] See William Lane Craig, On Guard: Defending Your Faith with Reason and Precision, (Colorado Springs, David C Cook, 2010), Ch. 6 for a much more detailed study of this argument.
[2] Evolutionary bioethicists like Peter Singer would disagree as this disrupts “survival of the fittest” by not killing off weak members of society. It’s more than a little disturbing that the New Yorker called Singer the planet’s “most influential living philosopher”. See why here.
[2] “Morality”, American Heritage Dictionary, 5th Ed., 2014.
[4]J. Budziszewski, Written on the Heart: The Case for Natural Law (Downers Grove, 111.: InterVarsity Press, 1997), p. 208-20, as quoted in I Don’t Have Enough Faith to Be an Atheist, by Frank Turek, p. 171.

The Cosmological Argument

Spiral Galaxy NGC 1566, courtesy www.nasa.govThe Cosmological Argument is not one argument, but rather a group of several arguments for the existence of God proposed by different thinkers over the centuries. Here is one relatively simple form of it –  just 2 premises and the conclusion – but with a lot packed in those 2 premises, and a serious implication inferred by the seemingly modest conclusion. Whole books can be written on each point[1], but in a nutshell, it goes like this:

Premise 1) Whatever begins to exist has a cause.
Premise 2) The universe began to exist.
Conclusion) Therefore, the universe has a cause.

Premise 1 is simply the law of causality, (i.e. cause and effect): the effect (beginning to exist) has a cause. This law is not only fundamental to science, but also verifiable by anyone through our everyday observations. Nobody walks into a room and, seeing a ball rolling across the room, assumes the ball has always been in motion. We instinctively look in the direction the ball rolled from to see who or what caused it to roll. Notice that this premise does not say that whatever exists has a cause, but that whatever begins to exist does. If either the theist’s God or the atheist’s universe is eternal, then neither would require a cause. Hence the atheist’s question of “Who made God?” is as irrelevant as asking them who made the universe in their view. No one needed to. That’s the nature of anything being eternal.

But Premise 2 then eliminates the option of an eternal universe through three independent lines of reasoning: one scientific and two philosophical. First, a host of scientific evidence points to the universe having a definite beginning. The Standard Cosmological Model (the “Big Bang”), whether you agree with the specifics of it or not, has withstood decades of attempted refutation and points to a unique beginning to all space and time at a single point in history, a singularity where space and time cease to exist prior to that point. Another insurmountable obstacle is the 2nd Law of Thermodynamics. This is the most universally accepted physical law, so much so that it forms the basis of the US Patent Office refusing to grant patents for perpetual motion machines without a working model. As Sir Arthur Eddington said, “if your theory is found to be against the second law of thermodynamics, I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”[2] The universe is only winding down. But if it is only winding down, that means it had be wound up.

Attacking the possibility of an eternal universe philosophically, we have two more abstract, but nevertheless valid, approaches. First, an eternal universe would require an infinite regress, but there can be no actual infinite regress because an actually infinite number of things cannot exist. A beginningless series of events in time entails an actually infinite number of things (events in this case). Therefore, a beginningless series of events in time cannot actually exist.

The second philosophical rationale is that one cannot traverse an infinite series. The series of events in time is a collection formed by adding one member (or event) after another. A collection formed by adding one member after another cannot be actually infinite.  So then, the series of events in time cannot be actually infinite.

Therefore, the universe has a cause. If this argument seemed fairly noncontroversial to you right from the beginning, then you might be surprised at the resistance to it. That’s because of the implications the conclusion leads us to. This cause cannot be material or temporal as space and time both had a beginning, and this first uncaused cause would necessarily have to exist before the effect it caused (the universe). This cause must be extremely powerful to cause everything observable (and probably more that we haven’t observed). The incredibly detailed precision observed in the universe would require an intellect far beyond the greatest human minds to orchestrate the intimately interrelated web of cause and effect detected so far. For comparison, we routinely fail to predict the consequences of even simple actions over periods of days or weeks (i.e. weather prediction). This cause is necessarily a free agent capable of making choices. An impersonal force like gravity cannot choose to act at a particular time on an object. A ball does not simply float in the air until gravity decides to act on it and make it fall to the ground. If this cause were simply a force like gravity, acting from all eternity, then the effect (the universe) would be eternal as well, which contradicts the observed evidence and our reasoning. This cause is therefore a person, in the general sense of a being possessing rationality. This first cause, or uncaused cause, then appears to be, for all practical purposes: eternal, omnipotent, omniscient, and personal. As with the Ontological Argument from last week, this correlates well with the description of God in the Bible and forces us to face the possibility of a sovereign Maker who might very well hold us accountable for our actions. Hence, the determined resistance to this line of reasoning.

[1] See “Reasonable Faith”, 3rd Ed., chapters 3 & 4, by William Lane Craig for a much more detailed treatment of this and other arguments for the existence of God.
[2] Sir Arthur Eddington, “The Nature of the Physical World”, 1927.

The Ontological Argument

The ThinkerLast week, I reviewed some key terms in logic as a prelude to looking at logical arguments for the existence of God. This first one is a philosophical rationale called the ontological argument. Ontology is simply the study of existence, or reality. And so the ontological argument is a line of reasoning based on the very nature of existence.

The first premise, or basis for this argument, is that it is at least possible that a maximally great being exists. This isn’t about what’s probable at this point – just what’s possible. It’s also not about whether we can know whether this being exists or not (epistemology), but simply about whether it could exist (ontology) . Now let’s define some terms. A “maximally great being” can be defined as a being possessing omniscience, omnipotence, and moral perfection. Omniscience is knowing all truth and only truth. Omnipotence is the ability to cause any effect not logically impossible. It is necessary, or noncontingent, existence. Moral perfection is the highest degree of moral attributes such as love, mercy, justice, etc. Where attributes conflict (i.e. mercy vs. justice), this being possesses the greatest compatible degree of each, such that any more of either trait could be considered an introduction of imperfection (i.e. the best possible combination). There is nothing self-contradictory about this concept. It is not like a square circle or a married bachelor. It is simply the spectrum of characteristics we observe in human beings extrapolated to a maximum value.

Premise 2 is that if it is possible that a maximally great being exists, then a maximally great being exists in some possible world. By “possible world”, we do not simply mean another planet, but rather any alternate reality with its own forms of matter & energy, laws of physics, existence or nonexistence of life, and even existence or nonexistence of space-time itself. The set of all possible worlds would be a set of all possible versions of reality; each with one, and only one, variable different from all others. For instance, one possible world may have a slightly different gravitational constant that results in the collapse of any conceivable universe, or the impossibility of the universe ever forming. Another might have every physical variable identical to the reality we are familiar with, but with a history where Hitler won WWII. This set of possible realities is necessarily immense (practically infinite) to address every possible physical and historical alternative.

Premise 3 proposes that if a maximally great being exists in some possible world, then it exists in every possible world. This one isn’t a very intuitive step, so let’s look at it a little closer. If a maximally great being in a possible world is indeed omnipotent, then all else in that possible world is contingent, or dependent on its existence. If it is morally perfect, then it is capable of making conscious decisions, of exercising free will. In that case, this being could’ve chosen not to create anything, but simply to exist, alone. So if a maximally great being exists, there is a possible world such that only that being exists. This would then be the minimum qualification for a possible world. This being is then the “lowest common denominator” in all possible worlds (i.e. one variable in common to all, that cannot be negated without eliminating that world from the set of all possible worlds). Therefore, Premise 3 logically follows, and the maximally great being exists in all possible worlds.

Premise 4 states that if a maximally great being exists in every possible world, then it exists in the actual world. What applies to the set as a whole applies to all members of the set. In logic, this is called “dictum de omni”, or the law about all – whatever is universally true of a subject must be true of everything contained in that subject. The actual world is contained in the set of all possible worlds. Therefore, premise 4 logically follows.

Premise 5 simply adds that if a maximally great being exists in the actual world, then a maximally great being exists. Not too controversial. The actual world is what exists as opposed to possible worlds that only could exist. Anything shown to exist in this actual world therefore has actual existence.

From these 5 premises follows the conclusion that a maximally great being exists. At this point, we’ve simply concluded that some being with certain characteristics necessarily exists, but what do those characteristics tell us? A necessary or noncontingent being can exist outside of space and time and is therefore immaterial. An omnipotent being could create, or cause all contingent elements of reality to exist. An omniscient being would be capable of designing the incredibly complex and very interdependent “system of systems”  we recognize as our universe. A morally perfect being would have the authority to issue decrees, judge behavior, and reward or punish as appropriate. This description aligns remarkably well with the biblical description of God, which leaves the reader with the choice of trying to refute the argument or admitting the existence of God and dealing with the consequences. Choose wisely.


Reasonable Faith, 3rd Ed., (Crossway Books, 2008), by William Lane Craig, Chapters 3 & 4. Craig’s interpretation of Alvin Plantinga’s refinement of St. Anselm’s ontological argument was a major part of my giving this argument another chance after discounting it for years. My only departure from Craig is that in premise 3, I’ve tried to justify the jump from existence in a possible world to existence in every world without resorting to the modal logic used by Plantinga and Craig.