What would you say if I told you I could mathematically prove that the summation of 2n as n approaches infinity is -1?  I can only imagine what you’re thinking. “Impossible!” “Liar!” “Blasphemy!” “Burn the witches!” Before you start chopping wood for my fire pit, observe…

Step 1: Set A equal to our equation

Step 2: Multiply A by 2

Step 3: Solve 2A - A

Step 4: Do the math

Subtracting series A from series 2A means the 2’s cancel out, the 4’s cancel out, the 8’s cancel out, etc. etc. all the way to infinity, thus leaving (0 - 1) as the only meaningful subtraction in the equation. Since 2A - A = A and 0 - 1 = -1, that means:

Before I accept the Nobel prize, I must humbly divulge that I’ve broken a small mathematical rule here even though it may not be obvious to you-- I treated infinity like an actual number. Infinity is not a number; it is an abstract concept our minds have constructed to answer silly questions like, “How long is a circle?” and “How much do I love my wife?” 

However, in the calculation above, you performed an operation on infinity (that of subtraction), thus treating the abstract concept of infinity as though it were a concrete number. This is a big no-no, not only in mathematics, but in logic and philosophy in general, which leads us to the cleverest and most often used logical fallacy you’ve probably never heard of… The Fallacy of Reification.

Also known as concretism, hypostatization, or the fallacy of misplaced concreteness, reification is the treatment of an abstract concept as though it were concrete, a real event, or a physical entity. The essence of “treatment” here is actually quite broad; for all intents and purposes, you are logically banned from performing any sort of operation on an abstract concept, up to and including the granddaddy operation of them all… the assertion of actual existence.

Does this reek of philosophy? I don’t blame you for pinching your nose; the fallacy of reification is one of the primary reasons many people feel exhausted after debating in that arena, as philosophy tends to jump from abstract to concrete like it was skipping rope. But this is an atheist website, so how is reification relevant here? The answer, my clever reader, is coming up next…

Have you ever stumbled across the Transcendental Argument for God, also referred to as TAG? This particular argument is currently championed by Matt Slick, Eric Hovind and Sye Ten Bruggencate, though many other apologists like to borrow its concepts from time to time. The essence of the argument is as follows: the only means we have for believing the validity of our reasoning is by assessing its validity using our reasoning. Since this is circular, we can never know for sure that our reasoning is valid, and thus we require a divine being to tell us so… therefore god.  Like an extremely easy version of Where’s Waldo, I bet you have no trouble spotting the Reification Fallacy demonstrated here, now that you know what it looks like (hint: is reasoning an abstract or concrete concept?  Second hint: is validity an abstract or concrete concept?). 

Another easy example that you’ll hear in the TAG presentation goes like this: “Imagine this circle represents all possible knowledge [TAGist draws a circle]; how much would you say you have? [TAGist shades a part of that circle] So couldn’t something in this unshaded part prove that god exists?” I won’t get into the flaws of the argument itself, but I will happily point out the reification fallacy of treating “knowledge” as though it can be encapsulated in a circle and divided out like pizza.

Getting away from TAG now, in a recent facebook discussion with apologist author Nancy Pearcey, Mrs. Pearcey quoted herself from her book The Soul of Science: “The amazing “fit” of mathematical concepts to the physical world cries out for explanation—but without the assumption of divine creation by a reasonable God, there is no explanation.

Mathematicians must act on sheer faith—a faith that lacks any basis.” By making such a claim, Nancy seems to be suggesting that mathematical concepts could possibly *not* fit to the physical world (we can thank god that they do), which is a clear case of misplaced concreteness. Mathematics is merely an abstract concept we invented to describe the behavior of the physical world in a quantifiable way (much like logic); it is the water that takes the shape of its container and thus has no meaning outside of reality.

Where else do we see the reification fallacy? You may not even realize this, but most theistic arguments can’t even get off the ground if strict acknowledgement and restriction of the reification fallacy is enforced. The believer typically relies on “generally-accepted” definitions with concreting implications in order to make their points, and those of us on the other side extend them a huge favor by allowing this reification to slide.  Here are some common examples:

--“The supernatural realm…”
This is an abstract concept we’ve defined to mean an imaginary place where unnatural things happen. By its very definition, the supernatural realm is a fantasy; it cannot be treated as an actual place. Whenever a believer tries to talk to you about the goings on of the supernatural realm, ask them to describe or define it for you first.

--“The universe is designed/humans are designed.”
“Designed” is an abstract concept we use to mean not naturally-occurring. Without a basis for understanding “naturally-occurring”, we’d have no mechanism for determining whether something is designed. Whenever a believer tries to tell you the universe is designed, ask them what an undesigned universe looks like first.

--“The universe is rational.”
“Rational” is an abstract concept we use to convey: “consistent with how the universe operates”; it has no meaning without the universe to define it first. Whenever a believer tries to tell you the universe is rational, ask them what an irrational universe looks like first.

--“Objective morality exists.”
“Morality” is an abstract concept we use to measure the “rightness” or “wrongness” of a given action, both of which are also abstract concepts left up to subjective interpretation. Whenever a believer tries to tell you about objective morality, ask them to define “wrong”, or to give you an example of an objective moral truth (“objective” means it must be unconditional and unreliant on opinion).

Abuse of the Reification Fallacy has been running rampant for quite some time in religious debates/discussions. We must stop allowing this tactic to be employed by those who already think “God says so” is a valid argument. Will you join me in the fight against misplaced concreteness?