Physics, Therefore God (Part 1)
A Look at Certitude Based Upon Scientific and Philosophical Principles
Introduction, Definition of Certitude and Presentation of the Kalām
Knowing that we know things without danger of error is called certitude. A thinking subject can be said to have certitude if it holds a belief and is “supremely convinced of its truth”.[1] For Christians, the existence of God (as classically understood to be a spirt that is “necessarily eternal, perfectly free, omnipotent, omniscient, perfectly good, and the creator of all things”)[2] should be one of the beliefs held with the most certitude. But how does one have certitude?
Scholastics hold that there are many kinds of certitude. As explained by R. P. Phillips, certitude is “the firm assent of the mind to some knowable proposition without any fear of error”.[3] He further distinguishes between subjective and objective certitude as the two main categories. For the purposes of this paper, formal certitude (with its subdivision of certitude of evidence) and physical certitude will be achieved through the evidence presented here.
The Kalām Cosmological Argument (popularised and defended in recent times by William Lane Craig) and its supporting arguments provide certitude both from physical and philosophical angles. As Craig formulates it, the argument goes:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.[4]
First, let us attain certitude from the scientific perspective.
Cosmology and Mathematics
Cementing belief in the beginning of the universe is the Borde-Guth-Vilenkin Theorem. Simply put, the universe is constantly expanding, and if it is expanding, it must have a starting point. From the moment of the Big Bang, the universe has been expanding “uniformly in all directions”.[5] Craig explains: “…any universe which is, on average, in a state of cosmic expansion throughout its history cannot be infinite in the past, but must have a past spacetime boundary”.[6] Whether one is a young- or old-earth creationist, a subscriber to the Big Bang theory, or any other reasonable (non-past-eternal) theory regarding the beginning of the universe, there has to be a moment (singularity) at which the universe began in order for it to begin expanding. Vilenkin says: “the initial singularity is not avoidable”.[7] Even Stephen Hawking, as an atheist, could not find a workaround to a creative singularity.[8]
Besides the very direct and concrete evidence of the kalām, mathematics and science (especially physics) point to God’s existence. Craig says that “mathematics is the language of nature”,[9] and even the master doubter Descartes “does not mention mathematical truths when he finalizes the setting of the doubt experiment”.[10] In approximately 1941, Kurt Gödel developed a mathematical proof for God’s existence. While an in-depth explanation of it here would take this paper far beyond a reasonable scope, Gödel uses axioms, definitions, and theories to move from things having positive properties to the necessary existence of God.
Hilbert’s Hotel
Let us move to philosophical support for the kalām. Commenting on it from a metaphysical perspective, Craig states the obvious: “being does not come from non-being”.[11] While some (who do not like where the BGV theorem leads) still try to use “loop quantum gravity models, string models, [and] even closed time-like curves” to avoid the creative singularity, these introduce further scientific and philosophical inconsistencies.[12] There is also a metaphysical problem in assuming the universe was caused by an infinite series of past events. What comes next is one of Dr Craig’s more controversial arguments in support of the kalām. Referred to as the Hilbert’s Hotel Argument (HHA),[13] it tries to show that “the metaphysical absurdity of an actually infinite number of things existing precludes the possibility of a beginningless past”.[14] Hendrick tries to prove the HHA to be invalid (and Craig to be intellectually inconsistent) on the grounds of presentism. Craig often presents the HHA (in both lectures and debates) in the following way:
Hilbert first invites us to imagine a hotel with a finite number of rooms. He says let's suppose that all of the rooms are full, and suppose that a new guest shows up at the desk asking for a room. “Sorry,” the manager says, “all of the rooms are full.” And the new guest has to be turned away. But, Hilbert says, now let's suppose instead we have an infinite hotel with an infinite number of rooms. Let's suppose again that all the rooms are full. This is critical to understand. There is not a single vacant room in the entire infinite hotel – every room is occupied by some guest. Now let's suppose that a new guest shows up at the desk asking for a room. “Of course! Of course!” says the manager. And he proceeds to shift the guest who was in room 1 into room 2, the guest who was in room 2 into room 3, the guest who was in room 3 into room 4, and so on and so forth out to infinity. As a result of these transpositions, room 1 now becomes vacant and the new guest gratefully checks in. And yet, before he arrived, all the rooms were full. Even stranger, according to the mathematicians, there are no more people in the hotel than there were before the new guest checked in. But how can this be? We just saw the manager give him his keys and walk down the hall. How could there not be one more person in the hotel than before? But Hilbert's Hotel becomes even stranger. Now let's suppose, Hilbert says, that an infinite number of new guests arrive at the desk asking to check in. And remember – all the rooms are full. Every room is occupied.[4] “No problem! No problem!” says the manager. And he moves the guest who was in room 1 into room 2, the guest who was in room 2 into room 4, the guest who was in room 3 into room 6, moving every former guest into the room number twice his own. Since any number multiplied by 2 gets you an even number, all of the odd numbered rooms become vacant! And the infinity of new guests gratefully check in. Yet, before they arrived all the rooms were full. Again, according to the mathematicians, there are no more people in the hotel than before they checked in, even though there were just as many new guests as there were old guests. In fact, a proprietor could do this an infinite number of times and there would always be room for more guests and there would never be any more people in the hotel than before.[15]
Regarding time theory, presentism “holds that objects do not have temporal parts but exist wholly at a time”.[16] Put another way, “only present things exist”.[17] First taking a merely rational view of this, presentism does make the most sense. (Its main opponent, eternalism, holds “past, present, and future things exist”, while actualism says “only actual things exist”.[18]) Hendrick points to an earlier form of Craig’s argument (listed below) to bolster his criticism:
1. An actual infinite cannot exist.
2. A beginningless series of equal past intervals of time is an actual infinite.
3. Therefore, a beginningless series of equal past intervals of time cannot exist.[19]
This differs from the below argument in its construction based upon time intervals. Hendrick tries to argue that the statement “an actually infinite number of things cannot exist’” does not follow from the HHA, “at least if abstract objects count as ‘things’”.[20] (The debate on the reality of abstract objects is quite outside the scope of this paper. Suffice it to say that Craig, contra Oppy and others, does not affirm this.) Hendrick, however, tries to use Platonism to disprove the HHA, and therefore Craig’s position. He feels Craig does not provide a suitable argument against Platonism, preferring instead to rely on the HHA. While this might be a good objection, Hendrick stretches the bounds of reasonableness by saying: “Should we conclude that just because it would be absurd for an actually infinite number of hotel rooms, marbles, baseball cards, or books to exist, that it would be equally absurd for an actually infinite number of numbers to exist?”[21] Here it seems as though Hendrick is confusing real and abstract objects, as well as the differences between actual and potential infinites, so the intellectual weight of this objection is somewhat lacking.
Returning to the temporal aspect of this, Hendrick contrasts A- and B-Theories of time. For him, “[o]n the A-Theory of time, which is often referred to as the tensed or dynamic theory, there is a real, objective difference between past, present, and future.”[22] Hendrick puts Craig in the A-Theory/presentist camp, and indeed Craig has written favourably on the subject. But, Hendrick seems to think that if Craig is an intellectually honest presentist, he cannot hold to the conclusions of the HHA. Feser sees none of the problems that Hendrick sees, writing: “[A specific quote from Craig] is directed at philosophers who suggest that presentists, to be consistent, should give up the assumption that past-tensed statements are true, in favour of a ‘fictionalist’ thesis that we should regard such statements merely as if they were true”.[23] That is, past tense factual statements can be true without necessarily giving up belief in presentism for eternalism or some other theory.
This is in strict contrast to B-Theory, which for Hendrick seems mostly aligned to eternalism; “no point in time is ontologically privileged”.[24] The past is just as real as the present. Hendrick argues that belief in presentism cannot allow simultaneous belief in the absurdities shown by the HHA. He writes: “As a presentist, I would [remind Craig] that, in my view, past events don’t exist at all”, so therefore there would be no worry of an infinite number of them existing.[25] Hendrick here seems to commit the strawman fallacy, for that is not Craig’s argument! As explained in the previous paragraph, presentism does not contest the reality of past-tense claims, but contests this reality being understood in an eternalist sense. With both Craig’s and Feser’s understanding of presentism, the absurdities of the HHA, contra Hendrick, still hold.
Mathematically speaking, what does the HHA say? Mathematicians may object to Hilbert’s Hotel because of the conclusions it draws about infinity and related concepts. Mathematicians can usefully manipulate infinity and imaginary numbers, things which cannot have any real existence. Instead, philosophers assign these to a more conceptual existence. It seems that the only reason mathematicians have a problem with HHA is due to assuming real existence of these entities. This is where a philosopher’s distinction between actual and potential infinites becomes useful. Using Aristotle’s understanding, “the actual infinite is that whose infinitude exists, or is given, at some point in time. The potential infinite is that whose infinitude exists, or is given, over time”.[26] The actual infinite is what philosophers often have problems with, while the potential infinite is something mathematicians, theoretical physicians, and others manipulate every day. If potential infinites were not possible, then 1/3 in decimal form (0.) could not be said to be a real number, or to have any bearing on reality. J. Warner Wallace writes: “...not everything used in mathematics necessarily implies a direct correspondence with a physical ontology. Mathematical consistency and coherence doesn’t necessarily imply physical realization”.[27]
Dr Craig puts this in syllogistic format as follows:
1. An actually infinite number of things cannot exist.
2. A beginningless series of past events involves an actually infinite number of things.
3. Therefore, a beginningless series of past events cannot exist.[28]
This argument is important, as its conclusion plays a large part in the kalām. Craig’s understanding of actual and potential infinites is somewhat similar to traditional understandings but has its own subtleties. For him, an actual infinite is a “collection which has an actually infinite number of members in it”, while a potential infinite is a collection which is at every point finite but always growing toward infinity as a limit”.[29] While this might apply to the real world, an understanding of God cannot function according to these definitions because he is ontologically different from the rest of the universe, as Aquinas will explain below.
Whether or not the HHA is a mathematically valid argument, the philosophical conclusions it draws are undeniable. According to Hilbert himself: “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to”.[30]
To be continued.
[1] Baron Reed, “Certainty”, at the Stanford Encyclopaedia of Philosophy (2022), at plato.stanford.edu.
[2] William Lane Craig, “Defining God’, at Reasonable Faith (18 April 2011), at reasonablefaith.org.
[3] R. P. Phillips, Modern Thomistic Philosophy vol. 2 (Heusenstamm: editiones scholasticae, 2013), 11-12.
[4] William Lane Craig, “In Defence of the Kalām Cosmological Argument”, in Faith and Philosophy 14, no. 2 (1997) 236-247, reproduced at Reasonable Faith, at reasonablefaith.org.
[5] “One of Hubble’s Key Projects Nails Down Nearly a Century of Uncertainty”, at NASA Hubblesite, at hubblesite.org.
[6] William Lane Craig, “Is There Evidence for God? William Lane Craig vs. Kevin Scharp”, at Reasonable Faith (May 2016), at reasonablefaith.org.
[7] Audrey Mithani and Alexander Vilenkin, “Did the Universe Have a Beginning?”, at arXiv (20 April 2022), at arxiv.org.
[8] Stephen Hawking, “The Origin of the Universe”, at Stephen Hawking (2005), at hawking.org.uk.
[9] Craig, “Is There Evidence for God?”, at reasonablefaith.org.
[10] Halil Turan, “The Cartesian Doubt Experiment and Mathematics”, at Paideia (1998), at bu.edu.
[11] William Lane Craig, “The Cosmological Argument (part 2)”
[12] Some even try to argue that the universe “bounces”, saying that it expanded and contracted to a certain point before expanding again into the present universe. James Riordon explains quite well the scientific implications (and impossibility) of these models. See James Riordon, “The Universe Began With a Bang, Not a Bounce, New Studies Find”, at Scientific American (24 May 2023), at scientificamerican.com.
[13] See Landon Hendrick, “Heartbreak at Hilbert’s Hotel”, University of Nebraska-Lincoln (2014), at digitalcommons.unl.edu.
[14] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[15] William Lane Craig, “The Cosmological Argument (part 2), at Reasonable Faith (20 August 2007), at reasonablefaith.org.
[16] William Lane Craig, “Presentism and Past Existence”, at Reasonable Faith (13 March 2016), at reasonablefaith.org.
[17] David Ingram and Jonathan Tallant, “Presentism”, at Stanford Encyclopedia of Philosophy (22 January 2018), at plato.stanford.edu.
[18] Ingram and Tallant, “Presentism”, at plato.stanford.edu.
[19] Quoted in Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[20] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[21] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[22] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[23] Edward Feser, “Craig Contra the Truthmaker Objection to Presentism”, at Edward Feser (20 March 2020), at edwardfeser.blogspot.com.
[24] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[25] Hendrick, “Heartbreak at Hilbert’s Hotel”, at digitalcommons.unl.edu.
[26] A.W. Moore, “Infinity”, at Routledge Encyclopaedia of Philosophy (1998), at rep.routledge.com.
[27] J. Warner Wallace, “Philosophical Arguments That the Universe Had a Beginning”, at CrossExamined (16 June 2014), at crossexamined.org.
[28] William Lane Craig, “The Cosmological Argument (part 2)”, at reasonablefaith.org.
[29] Craig, “The Cosmological Argument (part 2)”, at reasonablefaith.org.