Tag Archives: Logic

Divine Design (The Teleological Argument)

Leave a comment

London Museum Roof SmallWe’ve been looking at different explanations for the existence of God, and this week we have one that resonates with me as an engineer: the teleological argument, or argument from design comes from the Greek word “telos” meaning end purpose or goal. The argument is as follows:
Premise 1: Every design has a designer.
Premise 2: The universe was designed.
Conclusion: Therefore, the universe had a Designer.

Now let’s unpack those tidy little premises. Does every design have to have a designer? Design can be defined as: “a specification of an object (or process), manifested by an agent, intended to accomplish goals, in a particular environment, using a set of primitive components, satisfying a set of requirements, subject to constraints.” Though a bit dry, this actually describes my daily tasks as an engineer pretty well. But notice that design is defined as being “manifested by an agent”. It appears that designs have designers by definition. But even without the word “agent” in there, we can see that design requires intent – an end purpose, a goal. But goals require consciousness to make choices between alternatives. Processes like natural selection, unguided by conscious agents, can only “choose” alternatives that confer immediate advantage. For example, chess moves that sacrifice an immediate advantage for a long-term gain are not possible without the foresight of design. Chance and physical necessity also can’t explain evidence of design such as intent. Therefore, the indication of long-range intent is confirmation of a designer.

The second premise is perhaps more controversial. But let’s follow the evidence along 3 lines: terrestrial, cosmic, and biological design. First, many parameters on earth appear to be fine-tuned for life to exist, and not just any life, but large, complex life. Things like atmospheric transparency, oxygen content, the polarity of the water molecule, and the temperature of max density of water, among a variety of other dispersed parameters, appear to all be set to values in very narrow ranges that allow for our level of life to exist (and flourish). Second, although these values all fall in narrow ranges, we find in the universe parameters that are even more precisely balanced in favor of life. But these parameters are fine-tuned not just for life anywhere in the universe, but specifically for life on earth. Properties such as the speed of light, the ratio of proton to electron mass, the mass density, expansion rate, homogeneity, and entropy level of the universe, the  uniformity of radiation, the values of the four fundamental forces (gravity, electromagnetism, and the strong and weak nuclear forces), and the location of earth both in our galaxy and the Milky Way’s location in the universe, are some of the roughly 100 interdependent parameters that have to be what they are for us to exist.[1] Interestingly, we also happen to be in a unique position in the universe to even be able to see the evidence of this design.

Third, the structure and information content of DNA points to extremely information-centric design. Four DNA bases are the optimum number for speed of replication.[2] From a data storage standpoint, the 4 letter “alphabet” and 3 letter “words” used by DNA for synthesizing proteins are the most efficient system possible in terms of minimizing space requirements in the cell, simplifying encoding/decoding of the data, and maximizing redundancy for error checking.[3] DNA exhibits nested encoding where the same stored data is used to convey meaningful information when read one way, and different meaningful information when read a different way.[4] To understand the significance of this coding accomplishment, try writing a book that tells one story when read in order, and a different, but still intelligible, story when reading only every third word. This increases the storage capacity of DNA immensely. Even so, DNA does not have all of the information needed to assemble an organism in it.[5] Some of the information is stored outside the DNA, which leads to a chicken-and-egg problem of how the cell is built by plans stored in the DNA, but with instructions stored in the cell that’s being built using the DNA plans. Our planet, our universe, and even our own bodies appear to all show signs of design, making the second premise true.

If these 2 premises are true, then the conclusion is true that the universe had to have a designer. What characteristics could we infer about this designer from the conclusion?

  • Intelligence – far beyond that of any human designer to understand complex and interdependent “systems of systems” comprising the universe.
  • Foreknowledge – far beyond any human ability to anticipate highly complex interactions and plan for those contingencies.
  • Power – far beyond any human capacity to alter our surroundings (we celebrate when we figure out how to copy something in nature successfully; making all of nature from scratch is in a whole other league of accomplishment).
  • Intemporality and immateriality – no design precedes it’s designer. If the universe (and therefore all of space and time) had a designer, then that designer had to precede the universe. Therefore the designer would have to exist outside of space and time.
  • Benevolence – It’s relatively easy to imagine many ways our universe could be organized that would result in life being a much harder, more miserable, existence for us. Also, the fact of our unique position in the universe to be able to see so much of it could be an example of a deliberately placed trail leading us back to this designer.

These correspond well with the omniscient, omnipotent, omnipresent, eternal, loving God of the Christian Bible. So then, how do we respond to this? We could a) accept the evidence left for us by this God, and seek after Him, b) deny the evidence having honest doubts, but attempt to offer an alternative that explains the evidence as well, or c) simply refuse to consider the evidence. Please, don’t be content with this last option.

[1] Hugh Ross, “Fine Tuning for Life in the Universe”, http://www.reasons.org/articles/fine-tuning-for-life-in-the-universe, accessed 2014/08/03.
[2] “Why is the Number of DNA Bases 4?”, by Bo Deng, Dept. of Mathematics, University of Nebraska – Lincoln. Published in the 2006 Bulletin of Mathematical Biology.
[3] Werner Gitt, Without Excuse (Atlanta: Creation Book Publishers, 2011), p. 162-166.
[4] Stephen Meyer, Signature in the Cell (New York: Harper Collins, 2009), p. 466.
[5]  ibid., p. 473-474.

The Cosmological Argument

Leave a comment

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

3 Comments

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 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.

Resources:

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.

Logic

Leave a comment

Spock_at_consoleIn the coming weeks, I want to look at some different arguments for the existence of God. But first, how can you know my reasons for believing God exists are legitimate? Maybe you don’t believe God exists, or maybe you simply don’t know. Likewise, how do I know if your reasons are legitimate? How do we discuss our opposing reasons (for this or anything else imaginable) on a level playing field? With that goal in mind, today let’s start out with a refresher (or introduction) to basic logic. Like a lot of foundational material, it may seem a little dry, but it really is the necessary foundation for any type of critical thinking. Underlined words are key terms in logic.

Let’s start with some clarification. An argument in logic is not a fight or quarrel, but rather a rational thought process using a series of statements (or propositions) called premises and conclusions. As such, there are some rules for making sure the conclusions you draw are legitimate. Just like in sports, these rules help ensure that the winner really did win fairly.

Propositions are simply statements that may be either the premises or the conclusion of an argument. While you may be trying to determine a reasonable answer to a question with an argument, you can’t have a question or a command for a premise, so these are always declarative sentences. Not to bring up bad memories of diagramming sentences in grade school grammar, but these statements need a subject and a predicate. The subject is just what you’re talking about, while the predicate is what you’re saying about it. The premises are  propositions that each propose a basis for the conclusion. They give your evidence. Premises can be either true or false.  “The city of Houston, Texas is located in the country of Australia.” is a false premise, while “Mars orbits around the sun.” would be a true premise. These premises use terms that can either be clear or unclear. A term is clear if it can be understood in only one sense. For instance, a person can use the word “hot” to describe: temperature (“It’s hot outside”), attractiveness (“She’s hot!”), or questionable legality (“He wrote a hot check”).  In this case, “hot” has equivocal meanings and wouldn’t be a good term to use in a premise unless we either defined it first, or the meaning was clear from the context. Some terms are not so obviously different  in their meanings, and many a misunderstanding has happened because of this issue of equivocation (using the same term in different ways).

The conclusion either necessarily follows from the premises and the argument is valid, or it doesn’t follow and is invalid. “All men are mortal. Socrates is a man. Therefore, Socrates is mortal.” is a classic example of a valid syllogism. A syllogism is your most basic argument: 2 premises and 1 conclusion showing a clear relationship between 3 terms. If it is true that all men are mortal, and Socrates is indeed a man, then Socrates simply must be mortal. This is an example of deductive reasoning, which generally moves from a universal principle to a specific application. Inductive reasoning, on the other hand, typically moves from specific observations to a more general conclusion. Valid deduction provides certainty in its conclusion, while induction only provides a degree of probability. Just because you’ve observed many similar cases doesn’t mean all cases will be similar (the exception would if you’ve actually observed all cases). Science typically uses inductive reasoning based on specific observations, hence the tendency of scientists and engineers to always qualify what they say with disclaimers.

Understanding the principles of logic is advantageous regardless of your educational background, your culture, or your beliefs because it provides a framework for knowing that what you believe is true. If your terms are clear, your premises are true, and your deductive argument valid, then your position is necessarily true and there can be no argument against it. Likewise, if your opponent’s argument doesn’t have ambiguous terms, a false premise, or a logical fallacy, then, to be honest, you must admit he’s right. The same goes for me. And so we now have a level playing field, with the same rules applicable to and acknowledged by, both sides. Maybe you’ve listened to a talk show where two opposing guests simply stated their own views over and over again and ignored the other side. Or they simply talked past each other louder and louder? Did you walk away feeling like it was just pointless discussing some issues? There is hope, and this is where logic shines. I encourage you to not simply stop at this short  glossary of logic, but to dig deeper, learn it, and apply it in your own life.

Resources:

Socratic Logic, Edition 3.1, by Peter Kreeft, (St. Augustine’s Press, 2010), which served as a reference for much of this. This is an actual logic textbook.

Being Logical: A Guide to Good Thinking, by D.Q. McInerny, (Random House, 2005), is also an excellent and very concise introduction to logic, and well-suited for a first exposure to logical principles.

“All roads lead to Rome”?

Leave a comment

5-road-roundaboutMany atheists will say that all religions are the same, that “religion” as some broad homogenous category “poisons everything”. Religion is not true, contradicts reason and science, is detrimental to us,  and should therefore be abandoned, they say. Relativism, a current philosophical fad which claims that nobody is objectively “right” (except the relativist, apparently), also claims that all religions are the same, but instead that they’re all equally good. Sincere belief in any of the different world religions (or even your own made-up religion), will get you into heaven/paradise/nirvana/etc.

Are all religions the same? Do “all paths lead to Rome” (or heaven, in this case)? Both the atheist and relativist claims seem to break down under closer examination. The atheist claim that religion poisons everything ignores all of the tremendous benefits to humankind done in the name of Christianity (i.e. hospitals, insane asylums, and orphanages were all distinctly Christian inventions to care for “the least of these” who were very disposable in Roman and Greek culture[1]). Simultaneously, they magnify things Christians (or those claiming to be Christians) have done in opposition to Christ’s teaching, or group together actions of other religions with Christianity to get a negative “lump sum”. By that logic, we could lump Rolls-Royces and the old Yugos together and say all cars are worthless junk. Clearly, that would be a hasty generalization. Meanwhile, the relativist claim is self-refuting. Mutually exclusive worldviews can’t all be true. Jesus Christ stated in no uncertain terms, “I am the way, and the truth, and the life; nobody comes to the Father, but through Me.”[2] Yet Islam claims Jesus was only a prophet – honorable, but nothing more.[3] B’ahai claims He was a “manifestation of God, but not, in essence, God”. Judaism views Him as a blaspheming rabbi who claimed wrongly to be God and was justly killed for it. Other religions are happy to claim Jesus as only a prophet, teacher, or sage. Likewise, while religions will generally agree that things like murder and stealing are wrong, they disagree significantly on key issues like the nature of God (or if there even is a “God” or gods, e.g. Buddhism, Hinduism) and the nature of an afterlife (i.e. individual entrance to heaven, or absorption into the Brahman and subsequent annihilation of individuality).  These simply cannot all be true.

I want to give one example that I think simultaneously addresses both the atheistic view of all religion being equally bad and the relativist view of them all being equally good.  The difference between Christianity and Islam can be best exemplified by their views on death: The faithful Christian says “I don’t seek death, but my death would be a worthwhile sacrifice if more people came to accept God’s free gift of  eternal life through Jesus Christ”, while the faithful Muslim seems to say “My death would be a worthwhile sacrifice if it condemned more unbelievers to death while guaranteeing my life in Paradise.” Big difference there. One seeks the benefit of others at the potential cost of one’s own life, while the other seeks one’s own benefit at the cost of others’ lives. Some may say that’s an oversimplification, but I think it corresponds well with the reality being observed in many parts of the world right now. For instance, Jesus said, “Greater love hath no man than this, that a man lay down his life for his friends”, and the apostle Paul said that such was his love for the Jews that he would be willing to be accursed – to forfeit his own salvation – if that could guarantee the salvation of his kinsmen. Compare that self-sacrificial spirit to Islam’s “blessings of the shahid” (martyrs), where dying in battle for the cause of Allah guarantees your entrance to Paradise, 72 virgins, riches and honor, and the ability to intercede for 70 of your relatives.[4] This is not hyperbole, but a guarantee of salvation for someone and their whole family at the expense of others.

In the end, all religions are not equally good or equally bad. Rather, one is true, and we must exercise discerning judgement so as not to be deceived. As the apostle John tells us, “test the spirits to see whether they are from God.”[5] The first step is recognizing the implications of one of the 3 fundamental laws of logic, the Law of noncontradiction, and not falling for the copout that all religion is the same.

[1] Alvin J. Schmidt, Under the Influence: How Christianity Transformed Civilization, (Zondervan, 2001), pp. 151-169.
[2] John 14:6, NASB.
[3] See Surahs 5:72-75, 5:116-117 in the Qur’an, among others.
[4] Compare Romans 9:3 for the Christian with the following Muslim hadiths, here, here, here,  here, and here.
[5] 1 John 4:1, NASB.

“You Can’t Handle the Truth!”

Leave a comment

cant-handle-the-truthIn the movie “A Few Good Men”, Tom Cruise and Jack Nicholson famously go back and forth in court with Nicholson finally shouting back from the witness stand the classic line “You can’t handle the truth!” The truth can certainly be a powerful, devastating force at times. But what is truth? The Bible records Pilate asking Jesus that very question almost 2,000 years ago.[1] It’s a big question, but let’s look at one small aspect now.

Truth can be defined as the “ideal or fundamental reality apart from and transcending perceived experience.”[2] This indicates that truth is not subjective since it “transcends perceived experience”. In other words, a statement is true when it corresponds to the object it describes rather than the perception of the observer. Hence, it may be described as objective truth. A color-blind person may incorrectly perceive some colors, but the actual color may be  independently verifiable by the wavelength of light being reflected from an object. That a particular apple’s appearance corresponds to what we call “red” is then objectively true regardless of how, or even if, we perceive it. Likewise, the statement that there is life on other planets may or may not be true; but if true, it will be because of such life existing and not because of our knowledge of it.

What then are we to make of claims today that “everything’s relative”, or that something may be “true for you, but not for me”? First, isn’t it a little ironic to use an absolute term like “everything” to deny absolutes? In fact, both of these statements are actually self-refuting. They “commit suicide” as Greg Koukl would say. What’s implicit in the relativist’s first statements is that everything is relative except their absolute statement. How convenient. But “everything” includes that statement, which puts it in the same category as saying “white is black”. Their 2nd  claim implies that statements may be simultaneously true and false for 2 different people, except for their statement that is assumed to apply equally for everyone. But I can simply apply the claim to itself and say that “true for you, but not for me” is exactly that – not true for me – and ignore it. Ideas have consequences, and because of this self-refuting nature, the concept of relative truth can lead to very real absurdities. Bob may sincerely believe that he can jump off a cliff and fly (without a hang glider or other aid), while his friend John sincerely believes he can’t and pleads with Bob not to jump. Is this a case of “true for Bob, but not for John”? Is John wrong to try to help his friend see his error?  Applying his knowledge of physics and its correspondence to reality to the situation tells John his belief that John will plunge to his death would actually be true for both of them, in spite of Bob’s sincerity to the contrary. That Bob cannot fly on his own is true for all people, for all time, and in all places. That is the nature of truth; we do not create it by our beliefs or statements, but rather discover it.

We can determine when statements about our material world are true (i.e. the law of gravity) by testing them. But what about immaterial truth claims? Are these actual truths or simply opinions? Can we test for truth? Yes. A true statement will always satisfy the 3 fundamental laws of logic[3]:
The law of identity – a statement is identical to itself and different from another statement. A thing is what it is. Saying “Hitler was evil” and saying “Hitler was good” are not equivalent!
The law of noncontradiction – a statement cannot be both true and false at the same time in the same way. For a very clear (if somewhat harsh) verification of this law, the medieval Muslim philosopher Avicenna proposed this demonstration: “Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”[4]
The law of excluded middle – a statement is either true, or its negation is true. There is no middle state between existing and not existing.

There are other tests for truth, but these are foundational prerequisites, for no matter how coherent or comforting a claim is, if it fails these tests, it simply can’t be true. And this is how “relative truth” fails.

[1] John 18:38, NASB.
[2] “Truth”, Webster’s Encyclopedic Unabridged Dictionary of the English Language,  1996 ed.
[3] J.P. Moreland & William Lane Craig, Philosophical Foundations for a Christian Worldview, (InterVarsity Press, 2003), p. 132. See also D.Q. McInerny, Being Logical, (Random House, 2005), p. 26-28.
[4] Avicenna, The Book of Healing, Part IV, Metaphysics I, commenting on Aristotle, Topics I.11.105a4–5, published 1027.