Zero is a Mathematical Entity
Kevin R. Henke
October 19, 2022
In Henke (2022b), I stated:
“No gods, angels, demons or a Bible are also needed to figure out how people should try to function in our environments. We should develop rules (morality) through reason and not Biblical dogma so that we can live peacefully with each other and our environment.”
Lundahl (2022j) then replies to my statements:
“The morality is here said to be rooted in reason. Now, the question is not whether an agency external to our reason is needed to enlighten it - it may be the case, and as Christians, both Lewis and I believe after the fall each has some kind of need of that. The questions are rather:
· where do universally valid rules of reason come from?
· does reason deal with any moral rules prior to its own developing of moral rules?
The point of chapters 3 and (I think) 4 is, the laws of chemistry and electronics and physics and the constraints of evolution do not put us into the reach of discovering what is universally valid. For our reason to do this, we need to be more than that. The sentence ‘[o]ur brains, thoughts and surroundings are all ultimately controlled by the laws of chemistry and physics,’ needs to be false, at least if implying ‘and nothing else.’”
In Henke (2022ay), I answered Mr. Lundahl’s question: “Where do universally valid rules of reason come from”:
“The “universally valid rules of reason” that Lundahl (2022j) references are solely human discoveries. There’s no need for anything beyond human reason (Dennett 2006). The rules are “universal” because they happen to work in a variety of circumstances from generation to generation. In ancient times, humans learned to develop morals so that members of the tribe could get along with each other. Otherwise, the tribe would fall apart. People needed to cooperate with each other to survive. They also learned how to make spears, avoid the berries that were poisonous, develop strategies for hunting, etc. Both of their technological and socialization (moral) skills came from reasoning and they passed that knowledge onto their children. Their children added to the knowledge and passed that onto their children, etc. In other words, ancient people discovered morality in the same way that they discovered how to make a spear – through reason and trial and error.
In more modern times, we discovered that slavery was not a good idea from rational debate and empathy for our fellow human beings, and certainly not from prayer and the Bible (Avalos 2011). We also learned that it’s not a good idea to dump toxins into the atmosphere and oceans. Through physics, chemistry and biology, we learned that pollution may not just “go away.” Each generation learns valuable and often painful lessons through reason, trail and error, and debate, and we try to pass that wisdom and knowledge unto the next generation along with our positive technological advances. There’s no evidence that any of our advances in reasoning and technology came from God or something ‘beyond Nature.’
As for the Fall of Adam and Eve that Lundahl (2022j) and Lewis (1960) mention, there’s not a shred of evidence to support it. The young-Earth creationist version of the Fall is especially silly, where stars in distant galaxies supposedly become supernovae solely because Adam and Eve listened to a Talking Snake in Genesis 3, ate the wrong piece of fruit, and plunged the entire Universe into chaos and destruction.
When humans rationalize, we first observe and identify a problem or a mystery. We then thoroughly confirm our observations with more and independent observations from other humans. Did they really do or say that? Did that really happen? Over time through testing, trial and error, and being empathetic to our fellow humans, we developed “universally valid rules of reason”, which are the products of human activity. We then use the rules we’ve learned to solve additional problems and mysteries. The evidence indicates that we humans have no gods, angels or extraterrestrial intelligences helping us. We are alone and we are most effective in solving mysteries and problems when we work together and engage in science, evaluate historical data for accuracy, develop and use mathematics/logic, and strive to come to a consensus through rational debate and not through prayer, prophecy, astrology or other nonsensical methods.
As an example of humans using reason to solve a problem, Russia recently threatened Finland if they joined NATO. Even if the threat was nothing more than a bluff, because of the invasion of Ukraine, the Finnish government took the threat seriously. So, how did Finland respond? Did the Finnish government call for their people to engage in fasting and prayer to deal with the Russian threat? As far as I know, no. No doubt, there were certainly people in Finland that prayed for God to deliver them from the Soviets in 1939-1940 and 1941-1944. That didn’t work. Finland lost those wars and they lost a lot of lives and territory to the Soviets. So, the majority of Finns were probably smart enough not to try the religious options again. Instead, the history of 1939-1944 told them that their military could not stand up to Russia alone. Joining NATO was the logical option. The Finnish government and people recognized that forming an alliance with the nuclear powers of the USA and United Kingdom, as well as the rest of NATO, and not prayer, would be the best deterrent to Russian aggression. The Finns also recognized that a tyrant like Putin could not be trusted to keep any peace treaty or honor any other diplomatic settlement. There would be no “peace in our time” with Putin. Tyrants, like Putin, see diplomacy and being nice as weaknesses and they exploit agreements. Tyrants only respect their opponents when their opponents have extensive military power and a capability of destroying them. The goal of the Finns is to deter Russia and prevent a war. Finland becoming part of the NATO alliance is the best and most rational alternative for maintaining their peace and security. The Finns recognized what every child on the playground or our ancestors in the caves discovered long ago, it’s rational to have powerful friends if you’re being bullied or threatened.
As I previously stated in Henke (2022ai), as far as cosmologists and astronomers know, the laws of chemistry and physics are universal. They’ve found no exceptions. Newton’s Universal Law of Gravitation is indeed universal and explains the gravitational relationships between even the most distant stars and galaxies. Spectral analyses of stars have the same elements in them as we find on Earth (Delsemme 1998). So, chemistry is also universal. If Lewis (1960) and Mr. Lundahl want to say otherwise, the burden is on them to produce the evidence that the laws of chemistry and physics are not universal.
Humans invented mathematics and logic to quantify and describe how the Universe behaves, and to develop technologies to make our lives better. For example, geometry is essential in architecture. Mathematics did not come from the book of Numbers and there’s no evidence that God gave us mathematics and logic any more than Prometheus gave us fire. Interestingly, we see animals using primitive mathematics. Predators, for example, can tell the difference between a field without any prey and a field with a single prey. That is, they can tell the difference between zero and one. They can also tell the difference between one and many. If a cat in a field sees a single mouse on its left and a group of mice on its right, unless the single mouse is noticeably disabled, the cat is probably going to go after the group thinking it’s more likely to get a meal from one of them rather than trying to track down the mouse on the left and risk having it get away. So, predators going back to Tyrannosaurus rex and the Paleozoic seas were probably primitive counters. People simply expanded and improved mathematics/logic to solve different problems. There’s nothing supernatural here.” [my emphasis]
Lundahl (2022s) then replies to my bolded section in red:
Henke (2022ay): “Mathematics did not come from the book of Numbers…”
Lundahl (2022s): “Totally beside the point as far as CSL's [C.S. Lewis’] or my statements of the argument go. We never said it did.”
Correct, you did not say that. But, my statement reminds us that despite being the “chosen people of God”, the ancient Israelites showed no advanced knowledge of science or mathematics in their Bible (e.g., Babinski 2010).
Henke (2022ay): “Interestingly, we see animals using primitive mathematics. Predators, for example, can tell the difference between a field without any prey and a field with a single prey. That is, they can tell the difference between zero and one.”
“Zero is not a mathematical entity anyway.”
No! Zero is a mathematical entity. It’s a valid number. For example, it can be classified as an integer (Stewart 1991, p. 3). Zero is absolutely essential in calculus and other mathematics. How can I give the Miller Indices of a crystal without zero or negative numbers (Klein 2002, pp. 198-200)? Is Mr. Lundahl saying that because zero was not part of the formal mathematics of the ancient Romans or Greeks, or that the mathematical concept of zero is not specifically defined in the Bible, then it must not be all that important and should not be classified as a “mathematical entity”? Also, Mr. Lundahl seems to be somewhat fond of Roman numerals because he uses them for the months in the dates in his essays. Well, I would like to see Mr. Lundahl do calculus using the primitive and obsolete system of Roman numerals and without using zero or negative numbers.
References:
Avalos, H. 2011. Slavery, Abolitionism, and the Ethics of Biblical Scholarship: Sheffield Phoenix Press: Sheffield, UK, 331pp.
Babinski, E. 2010. “The Cosmology of the Bible” in J.W. Loftus (ed.) The Christian Delusion: Why Faith Fails: Prometheus Books: Amherst, NY, USA, pp. 109-147.
Delsemme, A. 1998. Our Cosmic Origins: From the Big Bang to the Emergence of Life and Intelligence: Cambridge University Press: Cambridge, UK, 322pp.
Dennett, D.C. 2006. Breaking the Spell: Religion as a Natural Phenomenon: Viking Penguin: London, UK, 448pp.
Klein, C. 2002. Mineral Science, 22nd edition, John Wiley & Sons: New York, USA, 641pp.
Lewis, C.S. 1960. Miracles, 2nd ed., printed 1974: Harper One: HarperCollinsPublishers, 294pp.
Stewart, J. 1991. Calculus, 2nd ed., Brooks/Cole Publishing Company: Pacific Grove, CA, USA.