# Boxing Pythagoras

## WLC on Time, Part 5: More Mathematical Misconceptions

After my last installment of this series, I had thought that I would be done critiquing Dr. William Lane Craig’s misunderstandings of the science and mathematics regarding time. After all, I’ve already shown that his arguments in support of the archaic Tensed Theory of Time are unfalsifiable, fallacious, ill-conceived, and self-contradictory. What more could there be for me to say? Well, in this week’s Reasonable Faith Podcast, Dr. Craig gifts me with more of his misconceptions about time. Starting at the 13:15 mark and lasting through the rest of the podcast, Dr. Craig addresses a question posed to him about the implications of the Tenseless Theory of Time on the theory of Evolution by Natural Selection, which the questioner refers to as “the holy grail of atheism.” I’ll note that this questioner doesn’t seem to realize that even a great many devout Christians completely accept the veracity of Evolution by Natural Selection, and that it is no more an “atheist” theory than is the Pythagorean Theorem. However, the particular implications on evolutionary biology will take a back seat, today, to the more general implications which Dr. Craig claims are made by the Tenseless Theory of Time. Specifically, Dr. Craig asserts that nothing actually changes over time, on the Tenseless Theory. Dr. Craig’s logic seems to be as follows:

1. On the Tenseless Theory, all points in time– past, present, and future– are equally real.
2. A spatial object which exists at point A in the past cannot be the same spatial object which exists at point B in the present or future, since they do not share the same properties.
3. Therefore, no actual change occurs on the Tenseless Theory of Time.

Dr. Craig uses the example of a fireplace poker. At one end of the poker is a handle, and at the other end is a hooked point. We do not think of this poker as changing from a handle to a point, because the whole poker exists together. Unfortunately for Dr. Craig, his inability to comprehend mathematics has once again prevented him from seeing a fairly glaring and obvious problem with his analogy. The properties of the poker certainly do change from a handle to a point over the distance of its length! Change is a comparison of some measurable properties with respect to other measurable properties. Let me give an easier example to visualize what I mean.

Figure 1: A falling object

Let’s imagine that we are dropping a ball into a pit which is 1000 meters deep. The graph in Figure 1 represents this action. The x-axis tells us the distance from the top of the pit in meters. The t-axis measures the passage of time in seconds. The blue curve is the ball. Every point along the blue curve is equally real– the point at t=0 is just as real as the point at t=10. Does that mean that the ball at t=0 is not the same ball as the one at t=10? Of course not. Dr. Craig is committing a fallacy of composition, here. Individual points in the ball’s trajectory are not the ball. The ball is the set of all points in its space-time trajectory. Let’s put this in math terms. The ball is represented by the curve, which has the function $x=-9.8t^2$. The point $(0,0)$ lies on the curve, but this point is not the curve. Similarly, the point $(10, -980)$ lies on the curve, but this point is not the curve. The curve is all of the points which satisfy its function. Mathematically, when we talk about “change over time,” we are comparing the different values of which satisfy the function at given points in time. Similarly, when you are talking about your friend “Bob,” you are referring to an entity which encompasses a whole set of space-time coordinates. You aren’t specifically talking about the “Bob” that existed at precisely 12:34pm on June 16, 2014, GMT. So, when we say that a change in Bob has occurred over time (often colloquially shortened to just “Bob changed”) we mean that his properties at one given point in time are not the same as his properties in another given point in time. We’re not talking about two different Bob’s, because “Bob” refers to an entire set of points in space-time. William Lane Craig suffers from a terrible lack of comprehension, when it comes to mathematics. As such, he wildly misconstrues the implications which the Tenseless Theory of Time has on the concept of “change.” He seems completely locked into his archaic view, incapable of even attempting to treat time as a physical dimension. Dr. Craig has been researching the philosophy of time for quite a number of years, now. One would think that, in all that research, he might have taken a little bit of time to learn the mathematics necessary to competently discuss the subject.

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## 8 thoughts on “WLC on Time, Part 5: More Mathematical Misconceptions”

1. I just wanted to thank you for this series, it’s absolutely first rate.

Cheers!

• Thank you for the compliment! I’ve actually thoroughly enjoyed writing this series, and responding to Dr. Craig’s claims about time has caused me to really take the time to research and understand a number of topics for which I had only scant knowledge, previously. To give credit where credit is due, I might never have heard of G.J. Whitrow’s excellent book, “The Natural Philosophy of Time,” if not for the fact that Dr. Craig quote mines it in “Time and Eternity.”

• I am curious, though; (how) does Craig address the fact that if nothing ever changes, then ‘free will’ is Jabberwockian nonsense since one cannot make choices if nothing in the universe is ever altered in the first place? That, in fact, “accepting Jesus Christ” becomes utterly meaningless, since someone could no more go from not accepting Jesus to accepting him than Bob(t=0) being the same entity was Bob(t=1).

It seems like a overly-literal interpretation of the Ship of Theseus, without realizing that the point of that intuition pump is to point out that our concept of identity is, itself, a linguistic fiction draped over reality, not a magic spell which informs reality.

And as an aside: ironically, I think that Craig may be on to more than he actually realizes, since, if Susskind’s holographic model is correct, then all information contained within our singularity is ‘stored’ holographically at its ‘skin’ (I’m not sure what technical term to use there, as a naked singularity wouldn’t have an event horizon. I’ll have to read up on that.) Since any one data point in a holographic interference pattern contains every data point in it, from that point of view, we are unitary holographs which represent our eigenvalues-over-time. But we’re also in the position of perceiving that there is a flow of time and that we do maintain something of a consistent point of view which we call ‘ego’. This isn’t a problem for me, since quantum duality seems to make that eminently possible; if photons are simultaneously both waves and particles, then we can simultaneously be both pure information stored holographically, and purely physical entities within the context of our spacetime continuum.

• I think that Dr. Craig would agree with your sentiment that the Tenseless Theory of Time eliminates free-will. He does not, himself, agree with the Tenseless theory. He was addressing it in response to a reader’s question.

I’m not overly familiar with Susskind’s holographic model, but I think I get the gist of your point here. I’ll have to do more reading on his ideas.

Thanks!

• My pleasure. If you’re interested in the holographic principle, this is a presentation I gave to my on-level physics class. I’ve got one that I gave to the AP classes, but unfortunately the video for both times crapped out. If you’d like, I have that ppt at the bottom of my webpage. Unfortunately I couldn’t upload it with videos, but I could send those along to you via links or files, if you’d like.

2. So I got into an argument with a Thomist about causality and its relationship to time. It was a very, very tedious discussion, but it led to a point of discussion that was interesting to me.

So he raised the idea of a cause/effect scenario in which the cause produced an effect that was, essentially, changeless (and this would be used to argue that causality could exist without time). So it was, essentially, cause x sustains the present state of some object. To illustrate this, he used a physical example: a person holding a baseball in it’s “present state” at a specific height off the ground.

I raised all kinds of objections to this, which essentially amounted to the fact that he was ignoring gravity and thermodynamics and his representation of the cause/effect relationship was overly simplistic because it also ignored the original state of the baseball and the person’s relationship to it–so much so that it rendered the original proposition of causality without change to be kind of absurd.

I’m fairly certain he couldn’t provide me a reason to suspect the idea was sensible. I was wondering if you ever heard of anything like that and what your thoughts were.

• I have not run across such an argument before, but I am inclined to agree with your line of reasoning, here. Holding a baseball at a specific height above the ground is not a changeless state. The holder is doing work, and thereby expending energy. This is an explicitly changing state.

• Right. Yet he kept insisting that although his example was, by his words, “physically impossible” that it didn’t mean it was always impossible (basically, I’m kind of summarizing to save time). I remember that when I explained he was ignoring gravity I told him that I could imagine a universe without gravity (in which there were no planets to hold a ball above) and he took this as proof that because I could imagine a universe without gravity, that his example stood.

And I’m thinking that there’s no real way to talk with a person like this. I want to know what are the properties of X that allow it to sustain Y. When you examine the example he gives, it’s not just one cause (when you look past the person and go onto a physiological or even a molecular level it’s many causes) and these don’t just produce one effect (the ball is held, energy is used, heat is created, waste products from muscle metabolism are created, etc.).

And to be fair, I asked for other examples that could illustrate his assertion (which was so weighed down by “act” and “potency” that I don’t even think he understood what he was saying). He claimed, repeatedly, that he didn’t need to because he already showed his assertion was possible.

I kind of used this to vent. I hope you don’t mind. It was frustrating.